Melting Snow while Backpacking

Introduction

I enjoy backpacking in the great outdoors. As all good backpackers know, planning for access to water is a critical part of any backpacking trip. Backpacking is a lot of work and usually involves a lot of sweating, so keeping hydrated is necessary. However, maintaining a backpack as light as possible is also a key consideration, so one doesn’t want to carry a lot of water around. Thus, the usual strategy is to stay close to natural sources of water and bring a good water filter to allow for regular refills of water containers.

As a side note, how much work is a backpacking trip, you ask? Oh, at 100% efficiency, almost one million Joules worth of work would be required on a typical mountainous trail with about 1,000 meters of up and down (average 5% grade for a 20 kilometer, or about 12.5 mile, trip) during the full trip. (That calculation is simply the potential energy, which is the mass multiplied by acceleration due to gravity multiplied by the total elevation change). However, considering the body is probably only about 5% efficient in this case, the real energy use is approximately 20 million Joules, which is equivalent to a total of 5,000 food calories. That is just the extra calories of food energy “burned” during the trip in addition to the resting metabolic calorie burn of about 2,000 calories per day.

While on a backpacking trip some time ago, my brother and I took a day hike up a mountain and we knew we would not be near any sources of water for a good portion of the day. I had two water bottles with me on the backpacking trip, one un-insulated bottle and one insulated Thermos bottle. However, I didn’t have enough foresight to bring a smaller bag on the trip to carry around for the day hike, so all I had was a plastic grocery sack (I know, some Californians reading this post will cringe at those words), and thus I only took one of my water bottles. Unfortunately, it turned out that I selected the wrong water bottle to take with me.

You see, even though I tried to ration my water intake, I found I was out of water with several miles left to hike. Fortunately, we found some snow that I ate a good amount of, and also packed a good amount into my water bottle. I figured it could melt as we went along our merry way and I would soon have some nice cool water to drink. Well, that didn’t work out as well as I hoped because the snow was painfully slow to melt. Ironically, as we continued our hike, we ended up in a downpour that lasted a few hours. So I was soaked to the bone and dehydrated at the same time, and I still couldn’t get the darn snow to melt in my water bottle!

I had plenty of time during the hike to think about methods to melt the snow into water so I could drink it. Since it relates to energy, I thought I would share my findings here. The underlying assumption below is that conduction heat transfer through the insulated water bottle was negligibly low in the short term, which I think turned out to be a pretty good assumption. Also, a spreadsheet containing the calculations is available below.

Air Blowing Method

My first thought was to simply blow air into the water bottle’s straw and have it come out the little pressure release hole. It would work like any basic heat exchanger. I could transfer heat from the air I exhaled into the snow and cause it to melt. We should all be somewhat familiar with heat exchangers, as many of us have at least two in/near our dwelling places as part of an air conditioning system. One heat exchanger (located inside) allows the transfer of heat from the air inside the living space into a refrigerant, and the other heat exchanger (located outside) allows the transfer of heat from the refrigerant to the outside air.

We can use a simple equation to determine how much air I would need to blow through my water bottle straw to melt the snow. To formulate this equation, I simply use the fact that the amount of heat required to melt the snow must be the same as the amount of heat lost by the air as it travels through the snow in the bottle.

Where

  • Q is the total amount of heat required to be transferred from the air to the snow, in Joules.
  • is the total mass of air required, in kilograms.
  • is the specific heat of air, which is 1.0 Joules per kilogram degrees Celsius.
  • is the change in temperature experienced by the air as it moves from my mouth to the exit hole, in degrees Celsius. I assume the air temperature goes from about 32 degrees Celsius when it exits my mouth to about 5 degrees Celsius when it exits the water bottle, for a change in temperature of 27 degrees C.
  • is the total mass of snow, in kilograms. My water bottle fits about 0.5 liters of water. I haven’t packed the snow in completely tight, so I have about 0.4 liters of snow at a density of about 0.6 kilograms per liter, for a total of 0.24 kilograms of snow.
  • is the latent heat of fusion ((Wikipedia link)) of water, which is 334,000 Joules per kilogram.

Now all we need to do is solve for to obtain how much air it would take going through the “heat exchanger” to melt the snow. However, just knowing the total mass of air required is not very helpful. What I really want to know is how long it will take to get that mass of air through the water bottle. Thus, I need to know my respiration rate. I need to know how much air (in units of mass, or kg) I can blow through the bottle in a given amount of time. A typical adult respiration rate is about 6 liters of air per minute. However, when I am hiking with a backpack on I am exercising relatively vigorously, so I probably have a respiration rate around 50 liters per minute.

At an altitude of about 6,000 feet above sea level, the density of air is about 1.0 kilograms per liter. Using all of this information and solving for the time required to melt the snow (see the spreadsheet attached below if you want to follow all the math there), I obtain:

So it would take me about an hour to get enough air through the water bottle to melt the snow. However, this assumes that all of the air I exhale goes through the water bottle. I found that to be unsustainable in practice, as the water bottle restricted my exhalations enough that I would quickly run out of breath (remember, I am hiking on mountains wearing a 35-pound backpack). So I could really only get about one third of the air I exhaled through the water bottle. That results in about three hours to melt the snow. I am not that patient.

Potential Energy Input Method

My next thought was to use potential energy of the snow to melt it. The thought process is relatively simple. When I held the water bottle upright, there was a small pocket of air at the top. So if I turned the water bottle over, there would be stored potential energy in the lump of snow because the snow tended to stick to the bottom of the bottle.

As you will recall, potential energy is stored mechanical energy. In this case, it is the energy of the snow that can be realized as the snow falls the short distance from one end of the water bottle to the other. That potential energy must go somewhere as the snow falls. Initially, some energy becomes kinetic energy as the snow moves. When the snow stops against the bottom end of the bottle, about the only place for that energy to go is in the form of heat to the snow. Bingo! All I have to do is tip the water bottle upside-down enough times and I convert enough potential energy into heat energy to melt the snow!

So how many times do I need to invert the water bottle? Using the equation from the previous example, I already know it takes about 80,000 Joules of energy to melt the snow. So I just need to figure out the amount of potential energy for the snow in one time of inverting the water bottle.

It turns out the potential energy is about 0.1 Joules. So I only need to invert the water bottle 850,000 times. Assuming I can invert the water bottle once per second, this ends up being about 10 days. I am definitely not that patient.

Shaking Method

So what if I could speed up the potential energy process with some kinetic energy instead? Instead of inverting the bottle and waiting for the snow to fall in the water bottle, I can just orient the bottle horizontally and shake it back and forth instead and get a similar effect. I can increase the rate of impacts between the snow and the inside of the water bottle and maybe even increase the amount of heat added to the snow on each impact.

Consider the physics of what is going on inside the bottle as I shake it back and forth. As I shake the bottle in one direction, the bottle and snow move together. Then as I move the bottle in the other direction, the snow slams into one end of the bottle. This motion can be represented as a sinusoidal function. All I need to know are the amplitude of the motion and the period of the motion and I can fully describe the maximum velocity and acceleration of the motion. I assume the total range of motion is about 20 centimeters and I can move the bottle back and forth about three times per second. Thus, the motion of the bottle can be represented in this plot:

The position, velocity, and acceleration of the bottle can be represented by these equations (with just some calculus magic going on in the background):

In these equations, A is the amplitude of the motion, which is 10 centimeters, and T is the period of the motion, or the time it takes to complete a full cycle of motion, which is 0.333 seconds. The maximum velocity of the bottle (represented by the first portion of the velocity equation) is about 2 meters per second and the maximum acceleration (again, represented by the first portion of the acceleration equation) is about 35 meters per second squared, or about 3.5 times the acceleration of gravity. Considering a major league baseball pitcher can move a baseball from zero to 95 miles per hour in about 0.3 seconds (acceleration of about 15 times that of gravity), that seems like a reasonable value for acceleration.

It is the maximum velocity that I am interested in since that feeds into the calculation of kinetic energy for each cycle of bottle motion. It turns out that the kinetic energy in one impact of snow using the shaking method is about four and a half times the potential energy of the snow using the gravity method. In addition, the rate of impacts is about six times the rate for the gravity method. Thus, the shaking method is about 27 times as efficient as the gravity method. Still, it would take about nine hours to melt the snow using the shaking method, and that is assuming my arms don’t fall off before that point as a result of doing that much shaking. Nine hours is still too long.

Conclusions

In conclusion, none of the methods I tried turned out to be very effective for melting snow inside the insulated water bottle. The amount of time calculated for each method is shown in the table below. For comparison, I considered how long it would take the snow to melt if I had an uninsulated container sitting in room temperature (with heat transfer via convection of the surrounding air), using similar analysis to a previous post. It turned out that that method would actually result in a shorter time to melt the snow than any of the other methods.

So how did I end up melting the snow? The truth is, I never got the snow fully melted during the backpacking trip. When I found that the snow was not melting in spite of my best efforts, I decided to try another experiment. I decided to see how long it would take the snow to melt inside the bottle. Sure enough, when I arrived home approximately 24 hours after I put the snow in the bottle, there was still a small amount of snow remaining. So an insulated water bottle is pretty effective at keeping a drink cold. And if you are out backpacking and see some snow you want to use for drinking water, I recommend using a fire to melt it!

If you are interested in the calculations, see this spreadsheet:

Backpacking Snow Melting CalculationsDownload

Energy Comparison: Driving versus Vacuuming

Introduction

This post is a continuation of a previous post to answer an additional example of an energy comparison. This calculation, like the previous one, deals with energy use in everyday life. The question we will start with is:

  • What takes more energy, driving your car to the grocery store or vacuuming the floors in your entire house?

Of course, the first thing you should think is the answer to every science and engineering question there is: “it depends.” In this case, the answer depends on a number of related questions, possibly including these:

  • To which grocery store am I driving? The close one or the one across town or in the nearest bigger city?
  • Which car am I driving? The small one with good fuel economy or my gas-guzzling truck?
  • How thoroughly will I vacuum the floors? Just a quick job to pick up anything visible or a full and complete job going over every square inch multiple times?

So, we need to make some reasonable assumptions. And once again, as in the previous example, we need to take the time to think about what we are actually measuring: useful energy or total energy consumed. As mentioned in the previous post, the conversion of energy is never perfectly efficient. So when we talk about energy, we need to be careful and deliberate about what quantity we are actually measuring or calculating. Are we calculating the energy to perform a task in an ideal (imaginary) system or in the real world? In this case, we are calculating the amount of energy that is purchased, not the amount of useful energy that is used. Thus, we will calculate the amount of energy stored in the gasoline that is used in the vehicle on one hand and the amount of electrical energy that is consumed from the grid on the other hand.

I will point out here that my goal in this post and pretty much all of my posts is not necessarily coming up with exact answers to the questions posed. My goal is to compare, to prompt more thinking, to explore the topics, and to get approximate answers. We need to approach problems differently for different situations. When human lives depend on the answers (which happens regularly in engineering, by the way, for calculations like structural members for bridges), then exactness and accuracy matter. Such is not the case with my calculations here. We are just exploring.

Thus, I will make the following reasonable assumptions about driving to the grocery store (and back home again):

  • The distance to the grocery store is 8 kilometers (that is about 5 miles, which is just slightly under the average distance to the nearest Walmart of 6.7 miles as explained in this interesting paper).
  • Fuel economy of the vehicle is 10.5 kilometers per liter of gasoline (about 25 miles per gallon, which is approximately the average in America).
  • The energy density of gasoline is 45 megajoules per kilogram (MJ/kg).
  • Vehicle efficiency (converting the chemical energy stored in gasoline to useful energy moving the vehicle) is 20%.

I will then make the following assumptions about vacuuming the house:

  • The surface area of flooring in the house is 190 square meters (based on average figures of new homes built over the past 40 years being about 2,000 square feet).
  • Only the carpet gets vacuumed.
  • The ratio of carpet to total flooring is 60% (based on flooring sales figures in 2006 and 2016).
  • About 60% of the carpet surface gets vacuumed (typical routine vacuuming doesn’t cover under furniture, etc.).
  • The carpet gets vacuumed at a rate of 0.2 square meters (about two square feet) per second. This is perhaps the most subjective assumption in the entire analysis, but this seems to be a reasonable rate.
  • The vacuum cleaner uses 1,000 watts of power when on.

Calculations

We can express the total amount of energy consumed by the vehicle in the trip to the grocery store in equation form as:

Where

  • E equals total chemical energy stored in the gasoline that is consumed, in Joules.
  • D equals the distance to the store, in kilometers.
  • G equals the energy density of the gasoline, in joules per kilogram.
  • equals the mass density of the gasoline, in kilograms per liter.
  • F equals the fuel economy of the vehicle, in kilometers per liter.

Plugging in the numbers, we obtain the following:

Note that this is the actual energy consumed, not the useful energy. Gasoline-powered vehicles are typically about 20% efficient, so if you could calculate just the mechanical energy it would take to move the car to the grocery store and back, it would be about 5 million Joules instead of 25 million Joules. All that extra energy doesn’t do anything useful to move the car, but it is energy that the driver has to purchase in the form of gasoline.

Switching gears (pun intended), we can express the total amount of energy consumed during vacuuming of the house in equation form as:

Where

  • equals the total electrical energy removed from the grid by the vacuum, in Joules.
  • P equals the (average) electrical power consumed by the vacuum during vacuuming, in Watts.
  • T equals the time required to do the vacuuming, in seconds.

And

Where

  • equals the total floor area of the house, in square meters.
  • equals the fraction of total flooring in the house that is carpet, unitless.
  • equals the fraction of total carpet that gets vacuumed, also unitless.
  • R equals the rate of vacuuming, in square meters per second.

Plugging in the numbers, we obtain the following:

Conclusions

As is obvious from the results above, driving to the grocery store takes a lot more energy than vacuuming the entire house. In fact, it takes about 70 times as much energy to drive to the grocery store than it does to vacuum the entire house. Did you realize traveling by vehicle was so energy intensive?

Now, let’s look at comparing to some other household uses of energy. In a previous post, I looked at the energy to lift a bag of potatoes up to the counter (about 100 Joules) and the energy to heat up about one liter of water to boiling temperature (about 400,000 Joules). Now, before we make any comparisons, we must first realize that in the previous post I considered the ideal case. That is, the amount of energy consumed in a perfect system, with no energy losses due to inefficiency or friction or anything else. Conversely, in this post, I am considering the actual energy used, as in, the energy contained in the “fuel” that gets used up.

Without going into too much detail and specifics, I will simply assert that it takes about 500 Joules of energy purchased (in the form of food) to perform 100 Joules worth of work to lift the bag of potatoes up to the counter. The assumption here is that the human body is approximately 20% efficient at converting food energy into mechanical energy.

Similarly, it takes about 570,000 Joules of energy purchased (in the form of electricity or natural gas for the stove) to heat up a liter of water to boiling temperature. That is, I assume that the stove is approximately 70% efficient at converting electrical or chemical energy into heat energy in the target substance (the water). In this case, most of the energy loss occurs not in converting electrical or chemical energy into heat (assuming the stove is modern enough that combustion is pretty well complete) but in heat loss to the surrounding environment.

To summarize, it takes approximately the same amount of energy to vacuum the entire house as it does to bring a quart of water to a boil. It takes significantly less energy to lift a bag of potatoes, and significantly more energy to drive to the grocery store and back. For easy comparison, see the table below.

Also, feel free to look at the simple calculations on this spreadsheet:

Vacuuming-and-Driving-CalculationsDownload

Energy and Exercise

Introduction

The topics of health and exercise are never far from many of our minds. It is definitely late enough in the year now that new year’s resolutions about exercise probably haven’t lasted this long. We are now well past the January spike in interest in gyms and gym memberships (as pointed out in this interesting article about the economics of gyms). But it is still a good time to explore the topic of the energy of exercise.

Hopefully most of us realize that food, exercise, health, and weight are all intertwined. Of course, those interactions and discussions get very complex and I can’t begin to scratch the surface of all that that entails. Thus, my purpose in this post is not to attempt to comment on all of the implications of energy and exercise. Rather, I will simply consider a few seemingly simple questions just for the joy of thinking about energy. The questions:

  • How much energy is used during exercise?
  • How is energy measured during exercise?

How Much Energy is Used during Exercise?

Often, this question is asked in the context of attempting to burn as many calories as possible so a person can lose weight. To answer this question, various tables have been put together with a quantification of the amount of energy “burned” by humans performing various activities including different forms of exercise. And not only exercise, but different types of activities in general. Of course, a person still burns some amount of energy even when sleeping or watching TV.

The following table shows how many food calories (about 4,184 joules per food calorie) a person weighing 155 pounds “typically” burns in half an hour of performing the listed activities. These calorie values are based on studies performed of people doing these exercises while metabolic rates are monitored. I found two sources for the information in the table, which mostly agreed, so may be from the same original source, but I included both just to show the comparison. The two sources were Harvard Medical School and website VeryWellFit.com.

Of course, I just selected a few of the many, many activities listed on these web sites, just to give a flavor. Obviously, there is a great deal of variation in the energy requirements of various exercise undertaken by humans. It is important to note, however, that the thing about a “typical” person performing “typical” exercise is that there is actually no such thing as “typical”. The actual energy burned during exercise varies significantly based on a variety of factors, some of the most prominent of which are the following:

  • Weight
  • Relative amount of different types of body mass
  • Actual activity rate

The first factor is weight. The more a person weighs, the more energy they burn off during exercise. In fact, for a typical person, energy burned is directly proportional to body weight. So a person who weighs 200 pounds would just need to multiply the numbers in the table by 1.3 (200 divided by 155) in order to get the number of calories they would burn performing that same activity. So, for example, a 200-pound person would use about 408 calories in half an hour bicycling compared to the 316 calories a 155-pound person would burn. This makes sense. It takes more energy to move more mass around, and it takes more energy to support more body tissue.

However, the second factor accounts for different types of body mass. There is a perception out there (which I maintained as well before doing some research) that a person with more muscle mass burns a lot more calories at rest than a person with more fat. It turns out that this isn’t as big of a factor as one might be led to believe. In fact, for a person at rest, typically at least 80% of energy consumption occurs in the major organs of the body (heart, lungs, kidneys, brain, and liver). See a good summary presenting this information in this article. Another good reference can be found here. Thus, the proportion of the body that is muscle tissue versus fat tissue is a relatively insignificant factor for total energy consumed at rest compared to the impressive metabolic rate of organ tissue.

The third factor is the actual activity rate maintained for a particular exercise. While the ratio of muscle mass to fat mass does not significantly effect resting metabolic rate, it can significantly affect daily activity rate. That is, a person with higher muscle mass will be more likely to have more active periods during the day and have higher metabolic rates during those active periods. It is pretty simple: the more muscle a person has, the more easy it is to be more active.

So, while a “typical” person weighing 155 pounds will burn 316 calories in a half hour of playing basketball, not all basketball is equal, and those casual playing will burn less energy than those involved in an intense game. Thus, the actual calories burned will vary significantly from the listed amounts in the table.

Of course, elite athletes will of course burn more energy than casual exercisers. This can be shown in an example from a book I read recently. While the table indicates that “vigorous” rowing still burns significantly less calories than running at a seven minutes per mile pace (316 versus 539 calories per half hour), rowing by an elite athlete might just be the most energy-demanding activity there is, as described in a quote in the book The Boys in the Boat:

The result of all this muscular effort [of rowing]… is that [a rower] burns calories and consumes oxygen at a rate that is unmatched in almost any other human endeavor. Physiologists, in fact, have calculated that rowing a two-thousand-meter race – the Olympic standard – takes the same physiological toll as playing two basketball games back-to-back. And it exacts that toll in about six minutes.
A well-conditioned oarsman or oarswoman competing at the highest levels must be able to take in and consume as much as eight liters of oxygen per minute; an average male is capable of taking in roughly four to five liters at most.

The Boys in the Boat, Daniel James Brown, Penguin Books, New York, 2013, pages 39-40.

While we all may not be able to become Olympic rowers, we all can control to some extent our metabolic activity rate through each day. This takes us to our next question, how is energy consumption during exercise (or any other activity for that matter) measured?

Measuring Metabolism

As one can imagine, the topic of measuring human body metabolism is vast and covers a lot of ground. We don’t have time to explore all of it in this blog post, but one useful topic for our consideration is the concept of the metabolic equivalent of task (MET). In order to understand the concept of MET, it is helpful to know that the average energy used by a person at rest is about one food calorie per kilogram of body weight each hour. Thus, a person who weighs 155 pounds (70 kilograms) uses 70 calories each hour. For 24 hours, that equals about 1700 calories.

Every nutrition facts label contains the statement “Percent Daily Values are based on a 2,000 calorie diet.” It is easy to see that a 2,000 calorie diet is derived from a typical person at rest for a day (1,700 calories) plus a few hundred more calories for being active beyond resting.

So while a MET can be defined in various ways, the most useful definition for our purposes is “the ratio of exercise metabolic rate to the resting metabolic rate.” So if a person is a couch potato all day, he would have a MET of 1.0 all through the day (and a MET of about 0.9 while sleeping, as activity level then is below the “resting rate”). So let’s look at our chart from earlier, this time in terms of METs instead of calories burned.

It is pretty astounding, at least to me anyway, that the human body can increase its rate of energy use by at least a factor of 15. Human bodies can be amazing energy-consuming machines when needed (or if that is your idea of fun). Of course, not everyone needs to be an elite athlete or maintain such high metabolic rates. The key to beneficial exercise is increasing METs in whatever ways are available.

The graph below shows a possible scenario for a person going throughout the day with different MET levels. Getting some exercise in first thing in the morning is a great idea. One could run for 10 minutes, or bike or row for 20 minutes, or do weightlifting for 30 minutes, or walk for 45 minutes. Any of those scenarios (assuming the remainder of the hour is spent “resting”) would result in an hourly average for the 6:00 to 7:00 a.m. hour of about 3 MET. Then maybe this person has a few opportunities in the day to take a walk or climb some stairs. Then when the person gets home from work, he does some chores or plays with the kids to get some increased metabolic activity.

The end result of the day shown in the chart is a total of 27.5 MET-hours, or about 3.5 MET-hours above the baseline level of 24. Increasing daily METs is a powerful method for overall better health and life satisfaction.

What about Fitness Trackers?

Maybe some of you have been thinking this question all along. Many these days wear little devices that can simply tell them exactly how much calories they have burned in a day. We can simply use a fitness tracker to tell us how much energy we are using in real time all the time, right?

Maybe. As with any data, we need to be cautious how we use it. As noted in this spot on National Public Radio, fitness trackers can have significant error in calculations of calories burned. Another study (summarized in another article on NPR) noted that people wearing fitness trackers actually lost less weight than those that didn’t, presumably due to the “look how many calories I burned, now I can eat a donut!” effect.

Conclusion

The human body has an amazing capacity for converting food into energy to be used at rest (mostly by our internal organs) and during all the various activities that people enjoy. I hope some of you will have a line graph of hourly average METs pop in your heads sometimes to remind you to do something enjoyable to get those METs up!

Should I Leave the Milk Out?

Introduction

For someone like me who constantly thinks about energy, even getting cold cereal ready to eat in the morning can be a mind-engaging task. As I pull the milk out of the refrigerator to pour on my cold cereal, I know I will probably want the milk again after I finish my cereal in order to pour myself a bowl of fresh milk to finish off my breakfast. The question always pops into my head, “should I leave the milk out, or put it back in the fridge until I need it again?” Of course, the correct answer to this question is, it doesn’t really matter. But for an energy enthusiast like me, I want the real answer. The answer that involves the least amount of energy wasted.

To reiterate, the two options, with respect to what happens with the fridge and the milk, are:

  • Option A: Open fridge (assume the fridge is open for about 5 seconds each time it is opened) and take milk out, leave the milk on the counter for 15 minutes, and then open fridge to return the milk.
  • Option B: Open fridge, close fridge for about 15 seconds while pouring milk, open fridge again to return the milk; 15 minutes later, open the fridge again to get the milk out, close fridge for 15 seconds while pouring milk, open fridge to return the milk.

So, the way I see it, it comes down to which option wastes more energy. Both options involve some “waste” of energy from the fridge when the fridge is opened to remove and return the milk. The “extra” energy wasted in Option A is the loss of coldness of the milk sitting on the counter for 15 minutes, while the extra energy wasted in Option B is the extra loss of cold air from the fridge when it is opened two additional times. So we just need to calculate the wasted energy.

We will make some assumptions as we go through these calculations, and the answers will vary based on the assumptions we make and the uncertainty in the numbers we use. Keep in mind that for this particular problem, we aren’t really looking for exact answers, we are looking for good enough answers that will allow us to compare the two options. Do both options result in about the same energy waste, or is one of them substantially greater than the other?

Another thing to keep in mind is that we aren’t just looking for the answer to this specific question, we are thinking about how this answer will apply to similar situations. What if what we are removing from the fridge isn’t milk, but something else? What if we are removing something from the freezer instead of the fridge? What if that something is out for an hour instead of just 15 minutes?

While we perform our calculations and compare values, we are looking at the broader picture, for rules to govern our use of the refrigerator in general. Can we come up with some good general ground rules and energy estimates that will make our future use of the refrigerator as efficient as possible? That is the goal.

Picture of a refrigerator packed with various contents, including milk.
Opening the fridge is always an adventure…

Internet Research

Now, before we go performing a bunch of calculations, we will check to see what the Internet says about this energy efficiency question. The topic that usually comes up under any searches about whether I should leave the milk out is food safety. The standard answer for how long milk can be left out of a refrigerator without spoiling seems to be about two hours. However, some Europeans normally leave their milk out of the fridge due to a different pasteurization process, though the percentage of milk of this type of milk that is consumed varies from country to country.

But that isn’t what we are looking for about energy efficiency. It turns out there are some ideas out there about how long the refrigerator door should be left open, such as this insightful question and answer post. There are also plenty of general energy saving tips for refrigerators and other kitchen appliances, but they don’t generally get into the details of how long or how often doors should be left open.

Calculation for Option “A” Energy Wasted

So it looks like we will just have to calculate the answers and see how things turn out. In the calculations below, I am assuming a full or nearly full gallon of milk. Let’s start with the extra energy wasted in Option A: the energy wasted with the milk sitting out on the counter. When the milk container sits out for 15 minutes, there are four ways that heat is being transferred into the milk:

  1. Convection heat transfer from the surrounding air,
  2. Conduction heat transfer through the surface the container is sitting on,
  3. Condensation of water vapor on the outside surface of the container, and
  4. Radiation heat transfer from the surrounding environment.
A graphic depicting four mechanisms by which heat is transferred into the milk and container: convection, conduction, radiation, and condensation.
Four mechanisms by which heat is transferred into the milk and container.

It is instructive to first consider the total amount of heat transfer required to occur to bring the entire gallon of milk up to room temperature. To calculate this, we simply use the heat equation:

Heat equation: Q equals m c delta T. Heat energy equals mass multiplied by specific heat capacity multiplied by the temperature difference.

The specific heat capacity of milk is approximately 3,790 joules per kilogram degrees Celsius, and one gallon of milk has a mass of 3.8 kilograms. Thus, the heat required is:

We can expect the heat transferred in 15 minutes to come well short of this value, as we know by experience that it takes at least a few hours for milk to get even close to room temperature. In starting my heat transfer calculations, I can immediately discount the effect of radiation heat transfer, as I know it is relatively very small in cases with relatively minimal difference in temperature (which would include this case with only 20 degrees Celsius difference).

Thus, I start by calculating convection heat transfer. Convection heat transfer calculations get fairly involved, so I will spare you the gory details of a slew of dimensionless numbers (including the Prandtl number, the Grashof number, the Nusselt number, the Rayleigh number, the Biot number, and the Fourier number) and strange correlations (including raising a factor to the power of 8/27). If you are interested, though, you can see my spreadsheet with the calculations attached below.

Suffice it to say, a good estimate for heat added to the milk via convection during the 15 minutes sitting on the counter is about 15,000 joules.

I can now calculate the conduction through the surface. I do this by using equations that assume the surface that the milk is sitting on is a semi-infinite solid. This assumption is reasonable in some situations but not others. I could attempt to use finite element analysis and numerical methods to come up with better answers, but instead I am just going to use engineering judgment to modify the answers into something reasonable based on what I know about the scenario. Anyway, it turns out that it matters a great deal what material the surface is made of. The table below shows the calculated energy transfer due to heat conduction in 15 minutes for different surfaces, along with my values modified to be more realistic.

Table of energy values in joules for different counter surfaces: steel at approximately 22,000 joules, granite at 12,500 joules, wood at 3,000 joules, and hot pad at 900 joules.

As the calculation indicates, the heat loss when the milk is sitting on steel is much greater (over 150 times greater!) than the heat loss when the milk is sitting on a hot pad, towel, or equivalent insulator. My modifications to make the values more realistic are based on the fact that the materials are not actually semi-infinite (there is a limited volume of material for the heat to be transferred into, which is particularly significant for the steel surface) and to account for the thermal resistance of the milk container and its contact with the surface. At any rate, a reasonable average value for heat loss considering a wide variety of counter top surfaces is approximately 5,000 joules.

Next, I can calculate the heat added to the milk as a result of condensation. The energy transferred as a result of condensation is simply the latent heat of vaporization of the mass of water being condensed from water vapor into liquid water on the surface of the milk container. Of course, the amount of condensation will vary significantly depending on the humidity content of the air. I made some reasonable estimates of the amount of condensation that will occur in my calculations (see full details in spreadsheet attached below) and came up with a figure of approximately 5,000 joules of heat transfer due to condensation.

So, in summary, for Option A, the wasted energy is:

Table showing wasted energy via four heat transfer mechanisms: convection at 15,000 joules, conduction at 5,000 joules, condensation at 5,000 joules, radiation being negligible for a total of 25,000 joules.

In case you are interested, see attached file for details of heat transfer calculations for this section:

Milk CalculationsDownload

Calculation for Option “B” Energy Wasted

Next, we can calculate how much energy is “wasted” when the fridge is opened. The “waste” that occurs when a refrigerator is opened is a result of the cold air inside the fridge being replaced with room temperature air from outside the fridge. The total interior volume of a typical fridge is approximately 0.3 to 0.5 cubic meters. However, some of that volume is taken up by the contents of the fridge, so maybe a good average number for air volume of a fridge is 0.25 cubic meters. The mass of that air is simply:

Mass of air equals volume multiplied by density.

V is the volume of the air in the fridge and ρ is the density of the air, with a typical value being 1.2 kilograms per cubic meter. Thus, the mass of air in a fridge is about 0.3 kg. To calculate the energy required to cool this air from room temperature (about 22 degrees Celsius) to fridge temperature (about 2 degrees Celsius), as in the previous section, we simply use the heat equation:

The specific heat capacity of air is approximately 1000 joules per kilogram degrees Celsius. Thus, the heat required is:

Another factor to consider is the water vapor within the air that enters the fridge. While humidity levels in the fridge and in the air outside the fridge can vary significantly, let us examine a typical scenario just to get an idea.

Say the air in your home is at 50% relative humidity and the air in the fridge is at 100% relative humidity (not an uncommon situation if the fridge has been opened recently or if there is anything wet in the fridge). According to this chart, that would mean replacing air in the fridge with 0.005 pounds of water per pound of air with air from the room with 0.008 pounds of water per pound of air. This is an extra 0.003 pounds of water per pound of air. Since we have 0.3 kg of air, that means approximately one gram of extra water vapor in the fridge.

That small amount of water vapor doesn’t seem like a big deal. However, it takes a relatively large amount of energy to condense that one gram of water vapor, about 2,000 joules in fact. If the air in the house is hot and/or humid, the energy required to condense the additional water vapor can exceed the energy required to cool the air itself.

So all together, we can estimate that the energy “wasted” when the air in the fridge is replaced with room temperature air is approximately 10,000 joules. Of course, that represents the situation in which the entire volume of air from the fridge is totally replaced with room-temperature air. Since the fridge door is only open for 5-10 seconds, maybe only one quarter to one third of the air is replaced. So, we can estimate that one fridge door opening is approximately 3,000 joules of wasted energy. So two extra fridge door openings result in approximately 6,000 joules of wasted energy.

(Note that in our scenario, both extra door opening occur just 15 seconds or so after the previous opening, so much of the energy loss due to opening the door would have already occurred. That is, the air in the fridge is already somewhere between normal fridge temperature and room temperature. Thus, the amount of energy waste is actually some value lower than 6,000 joules for the two extra fridge openings, but the 6,000 joules is still a reasonable estimate.)

Conclusions

For the specific scenario postulated in the introduction, leaving the milk out of the fridge for 15 minutes wastes more energy than opening the fridge door two extra times to put the milk back and get it out again (25,000 joules compared to 6,000 joules).

If the period of time for the milk to be out was reduced to four minutes, it would be a close call as to which option would waste more energy (both options wasting about 6,000 joules in that case). So four minutes is probably a good cut-off time. If a full gallon of milk will be out for any longer than four minutes, it is better to just open the fridge and put it back in, then get it out again later.

I should note here that the energy waste we have discussed above is not the same as the extra electrical energy required to run the refrigerator. Refrigerators have a typical coefficient of performance of three to four, meaning that for every joule of electrical energy used by the refrigerator, three to four joules of heat energy can be removed from the interior of the fridge. So for scenario above with 6,000 joules of wasted energy, the fridge may use about 2,000 joules of electrical energy. That is about the energy required to power a 60-watt light bulb for about 30 seconds. (Yes, I realize most “60-watt” light bulbs do not actually take 60 watts of electricity to run anymore due to the efficiency of compact fluorescent and LED bulbs).

In the end, perhaps opening the door of the fridge isn’t as bad as we might think in terms of energy efficiency. Once the fridge has been open for a while, though, the cooling system will kick on and the cool air will mostly be wasted immediately to outside the fridge. Since a typical fridge cooling system uses 100-125 watts to run, it only takes about 30 seconds of the fridge running to remove the amount of heat equivalent to replacing all the room temperature air in the fridge with normal fridge temperature air. However, if the fridge is left open for a while, all of that 100-125 watts of the fridge running is almost immediately wasted as cold air flows right out the door.

I should also note that the amount of energy wasted by a refrigerator varies with the season of the year. In the winter time, when energy is being used to heat a home anyway, energy used by the fridge to cool the interior space is put out into the home as heat. So the energy isn’t really wasted at all. A person could, in fact, heat their home just by leaving the door of the refrigerator open all the time, but this isn’t really recommended (as the food wouldn’t stay cold and the fridge probably wouldn’t last long running all the time). Also, for those that have natural gas furnaces, using the furnace to heat the home is much more efficient than using electricity (such as using a refrigerator).

However, in the summer time, when air conditioning is on, the energy wasted by the fridge causes even more energy waste than just that used by the fridge itself. The air conditioning system must work to remove the heat energy (which has been converted from electrical energy by the fridge) from the home. So if you are going to pick a time of year when you are really strict about saving energy for the refrigerator, pick summer time.

Perhaps the most notable energy efficiency tips for use of a fridge that are not immediately obvious are the following:

  • There is value in keeping the air in the fridge dry by not leaving standing water or wet, uncovered foods because it takes a relatively large amount of energy to condense water (compared to the relatively small amount of energy to cool air).
  • When items are removed from the fridge, consider placing them on a hot pad or towel instead of directly on a counter or table surface (especially if that surface is metal!).

In conclusion, I hope this post has spurred some thoughts about energy efficiency for refrigerators. I hope I have answered the question “should I leave the milk out?” Of course, while each of us acting individually can’t save a whole lot of energy based on how we use our refrigerators, maybe if we all tried to be just a little more efficient, our combined efforts would add up to a big impact in terms of less waste and a better overall world environment. That is the dream, anyway.

And one final note. If you enjoyed this post, you might also enjoy a somewhat related post that answers the question of what appliance wins between a freezer and a toaster. Enjoy.

Worldwide Human Energy Use

Introduction

Of particular interest in the topic of energy is the use of energy by humans. Much has been written and spoken on this subject. Each individual approaches the vast topic of “energy” from a different angle, having various life experiences and preconceived notions. In this post I will take the “30,000-foot” view. That is, I will look at the entire subject objectively from a far-removed viewpoint from which I can see the entire scope of the topic. Of course, it is impossible to consider a subject entirely objectively, for I have my own background and experiences that color my view of the world. But I will do my best.

To start with, since humans were humans, they have always used some form of energy to support human life. Obviously (or perhaps not so obviously today when we are so connected to and reliant on various forms of energy-dependent technology), the energy of primary concern for humans is biological metabolic processes. Each and every human being must eat to survive. With very few exceptions, you can be assured that every human being you see each day has had something to eat within the past week (most people just don’t go that long without eating, though most people can actually survive 4-6 weeks without food), and likely within the past day, and probably within the past six hours (the exception being in the morning because there are quite a few people who don’t eat breakfast, as shown in this survey as one source among many).

This is, to me, a remarkable thing. Each and every day, there are over seven and a half billion people that need to get enough food into their body to provide the energy their bodies need for the day’s activities. For those of us connected to modern economies, there is a massive behind-the-scenes effort going on every day to support our food needs, providing edible products to us from far-flung places around the globe which are processed in many locations far and near. Those living in subsistence economies are usually much more closely connected to their food sources and frequently grow much of their own food needs.

Energy Use by Human Society

While the topics of human metabolism and food production certainly deserve additional attention, it is to the more obvious aspects of the use of the word “energy” in connection with humans upon which we will place our focus. That is, the use of energy in human society external to the human body itself. So for the rest of this blog post, the word “energy” will mean energy used by humans not as part of the metabolic cycle (that is, not related to food).

In this context, the vast majority of energy used by humans throughout history has been used within the past few hundred years. Throughout early human history, energy use was limited to what people could find around them (mostly wood) to burn for purposes of cooking and staying warm. This is certainly a form of energy use.

I must here interject to distinguish between energy in general and useful energy. In an open fire there may be a significant amount of “chemical energy” stored in the chemical bonds of the burnable material that gets converted to heat energy. However, it is likely that not much of that energy is actually useful. On a hot day (when the heat energy of the fire is not needed to warm up the people standing around the fire), perhaps only 5% of the heat from the fire actually goes into cooking the food. On a cold day, the efficiency is slightly better (maybe 10%) because some of the energy is useful in providing warmth to people nearby. The rest of the 90-95% of the energy of the open fire just escapes as heat into the atmosphere.

Energy use has slowly grown more efficient over human history, and the number of people on the earth has increased dramatically in recent centuries, and the average energy used per person has also increased dramatically. So, it really is no exaggeration to say that the vast majority of (useful) energy consumed by humans has been within the past few hundred years.

Fossil Fuels Dominate Energy Use

And what has been the major source of that energy? Fossil fuels. Whether in solid (coal), liquid (petroleum), or gas (natural gas) form, fossil fuels have dominated the worldwide energy scene for over a hundred years.

At this point in this post, I am tempted to include a bunch of charts, tables, and graphs to best paint the picture of energy use by humans. However, this has already been performed by a number of parties far more thoroughly and compellingly than I could ever hope to do. There are entire government agencies dedicated to compiling, analyzing, and presenting energy statistics, including the United States Energy Information Administration. The International Energy Agency has a staff of over 200 dedicated to worldwide energy issues. Even other individuals (such as Vaclav Smil) have produced more energy charts than I could hope to reproduce.

I found two articles that do a pretty good job of showing energy use over the past few hundred years in chart form if you are interested:

For my purposes here, I will include just two charts and some commentary. First, let me note that there are many ways of categorizing energy production and use. Probably the most popular way to categorize energy use is by primary supply, that is, the source from whence the energy was harvested (for example, oil, coal, natural gas, nuclear, solar, wind, geothermal, biofuel, etc.). Other ways of categorizing energy include by economy sector (industrial, commercial, residential, and transportation) or by end use (building heating/cooling, different forms of transportation, etc.). Sometimes you can even find charts with multiple categorization schemes in the same chart, such as these from Lawrence Livermore National Laboratory. This chart gets even more detailed (as explained in this article, since the website itself doesn’t explain much).

Because there are so many ways to think about and categorize energy, one must be careful looking at these charts to make sure it is saying what one thinks it is saying. For example, one might say something like “nuclear energy provides 20% of the total energy consumed in the United States”, when in reality, nuclear energy is only 20% of the electricity consumed in the United States, which only makes up only about 40% of energy used in the United States, so the correct statement should be “nuclear energy provides about 8% of the total energy consumed in the United States”. So just be careful when looking at energy statistics because there are a lot of ways to get them wrong.

Now, the two charts I am choosing to include are the worldwide total primary energy supply in 1960 and again 50 years later in 2010. I think these tell the story of worldwide energy use as well as any. Data source is Our World in Data.

Worldwide Energy Sources in 1960: pie chart.
Worldwide Energy Sources in 2010: pie chart

Obviously, the total energy used in 2010 (about 140,000 terawatt-hours, or about 510 exajoules) is more than the energy used in 1960 (about 40,000 terawatt-hours, or about 150 exajoules). In fact, over that 50-year period, worldwide energy use increased by a factor of 3.5.

In 1960, the top two worldwide energy sources were coal (at 38%) and oil (at 27%). In 2010, the top two worldwide energy sources were oil (at 35%) and coal (at 30%). Those two sources together accounted for 65% of worldwide energy in 1960 and in 2010. Natural gas and traditional biofuels switched places, with natural gas going from 11% of energy in 1960 to 23% of energy in 2010 and biofuels going from 22% in 1960 to 8% in 2010. From 1960 to 2010, biofuel use increased by about 30%, while natural gas use increased by a factor of seven. Hydropower has maintained its position as a minor player in energy at about 2%. Nuclear-generated electricity has grown to provide about 2% of global energy. Renewables such as wind and solar made up about half of a percent of global energy in 2010.

One story these pie charts do not tell is the disparity in energy use around the world. For example, the average person in the United States uses about 20 times more energy than the average person in Ghana. And energy use within the United States isn’t equal either, as the rich use many times more energy per person than the poor. So, obviously, looking at entire world energy use alone is insufficient. If everyone in the world used as much energy as the average American, energy use would be drastically different.

We hear a lot about renewable energy these days. Energy produced by wind and solar has grown dramatically in recent years. However, wind and solar combined still only account for less than two percent of total world energy use. That is a lot of energy, and a lot of rapid growth in renewables, but it is still only a very small piece of the whole pie.

Nuclear energy has been proclaimed by various people at various times to be the solution to the world’s energy needs. Nuclear energy today is also only a very small piece of the pie. Abundant resources (uranium and thorium in ores) exist in the world to provide a lot of nuclear fission energy for the future, but there are political and economic challenges for wide expansion of nuclear energy. Nuclear fusion energy has been a hopeful subject in the energy picture for many years, but anyone who follows nuclear fusion knows that for about the past fifty years, the technology has always been about thirty years away from being a commercially viable energy source that can transform the way energy is generated for worldwide use.

The Worldwide Energy Future

So what will our energy future look like? Will earth’s population be able to shift from reliance on fossil fuels to some other alternative energy source? I can’t answer those questions, but I can point out a few thoughts for consideration.

First, the inherent difficulty in predicting the future. I always find it humorous to look at projections for future energy use right after data from past energy use (as in page 13 of this report). The past is rough and pointy, with ups and downs, while the future projections are smooth curves in predictable patterns. Of course, those that produce the projections know (or at least I hope they know) that the future will not be as smooth as their projections show. The future will be messy just like the past. We must continue to attempt to predict the future in order to plan for it, but at the same time we must realize that we will not be successful in attempting to predict the future and we will get a lot of things wrong.

There are many different visions for the future of energy, including rapid growth of renewables, rapid growth of nuclear power, curbing energy demand, etc. A central debate in considering the future of energy is whether energy will continue to be mass-produced or whether it will be more distributed. Should energy be produced on a large scale (big power plants for electricity and big oil wells and refineries for petroleum products) or by each individual user (small wind mills, solar panels, and even possibly “Mr. Fusion” units, or perhaps a more realistic alternative, home biogas reactors)? Can the production of energy be distributed in a similar manner to how the Internet has distributed information to every corner of the globe?

As we consider these questions, we need to keep in mind that energy is not like information. There have been rapid advances over the past few decades with information storage and transfer. Computers have revolutionized how information is produced, distributed, and stored. Can a similar revolution take place to revolutionize the energy economy? In reality, probably not. Energy is physically different from information and the laws of physics that apply are different. Energy storage and transfer simply involves more physical materials. So we can’t necessarily expect a revolution to occur in energy technology as has occurred in information technology. That doesn’t mean we shouldn’t try, though.

Climate Change

I simply can’t finish this post without making mention of climate change, which is probably the elephant in the “room” of this topic. Obviously, there is much discussion on this topic today and it can be difficult to go for long without hearing something about it. I, for one, feel it is a topic that should not be ignored. Of course, this topic has become, unfortunately, political. It can be difficult to get into this topic without alienating one side or the other of the political spectrum, but I will attempt to do so.

My coverage of this topic here will be short and completely insufficient. In short, whether or not one “believes” in climate change, there should be some things we can agree on:

  • We need to keep studying this topic. There are constantly arguments about whether or not the science on this topic is “settled” or “decided” or “beyond doubt”. The fact is, we don’t know everything about climate change but we do know enough that we know we need to figure out more about it.
  • Human action is causing significant changes to the “natural” state of the world. The fact is, humans are putting a lot of products into the atmosphere that have not been there in the past history of the earth.
  • Since we really don’t know for sure what all the stuff (often simplified to “carbon”) we are putting in the atmosphere does to the future climate of the earth (though we do have some pretty good ideas based on some science), we should take steps (recognizing other priorities and limitations) to limit our emissions.

I personally think there is a lot more we can be doing to limit emissions than we are currently doing. Everything we do now to understand climate change and limit its impact is an investment in the future of humanity.

Conclusion

Societal energy use has been dominated so far in human history by fossil fuels. The future of energy use in the world is uncertain.

Measuring Energy

How is energy measured? This is a great question, and deserves our attention in this post. As we consider how energy is measured, we will run into the most commonly used units of measurement for energy, joules (J), British thermal units (Btu), and watt-hours (Wh).

It turns out that measuring energy is difficult. Energy is not something that is readily accessible to our five senses. We can’t see, hear, touch, smell, or taste energy, at least not directly. Some properties of the world around us are readily available to our five senses, such as distance, mass and temperature. We can see physical dimensions that something has and can easily compare the size of one object to another. We can feel whether something is hot or cold.

Though we may not be able to see or touch something and immediately convert it to an exact dimension (as in, “I can see that this smartphone is exactly 15.3 centimeters long” or “I just walked outside and I can feel that the air temperature out here is exactly 10.7 degrees Celsius”), we can usually get pretty close (“this smartphone is between 10 and 20 centimeters long” or “the outside temperature is between 5 and 15 degrees Celsius”), and can almost always compare things like distance, mass, and temperature to know what things are bigger or hotter.

The same is not true of energy. We do not have an intuitive sense for energy like we do for other properties. Energy takes higher-level thinking. Consider these three examples:

  1. What takes more energy, lifting a 20-pound bag of potatoes from the floor to the kitchen counter or heating a small pot of water to boiling temperature?
  2. What takes more energy, driving your car to the grocery store or vacuuming the floors in your entire house?
  3. What releases more usable energy: one pellet of nuclear fuel (the size of an average marble) in a reactor in a nuclear power plant or 1,000 pounds of coal in a coal power plant?

Did you come up with the answers right away? How confident are you in your answers? Maybe you didn’t even hazard a guess because you just have no idea. I will share the answer to the first question later in this post (and the other two in a future post), but for now, let us consider why these questions may seem so difficult.

As mentioned, energy is not intuitively accessible to our immediate observations of the world around us. Thus, it wasn’t until the 1800s that the word “energy” was actually used in its modern sense of meaning, as a physical characteristic of an object or system that can actually be calculated and quantified. While it would be fascinating to dig into the history of the concept of energy, that is not my purpose here.

In order to understand how energy is measured, calculated, and quantified, it will be instructive to look at the meaning of some of the most widely used units of energy.

Units of Energy

The most widely-used unit of energy worldwide is the joule, named after James Prescott Joule, an English amateur scientist who lived from 1818 to 1889. A joule is equal to one kilogram meter squared per second squared, or one newton-meter. It is the amount of energy involved in moving with a force of one newton over a distance of one meter. The joule serves brilliantly within the overall International System of Units (also known as SI units) to measure various types of energy, including mechanical energy (kinetic or potential), chemical energy, and heat energy. The use of the joule is often the simplest method for completing energy conversions and calculations.

A watt-hour is a unit of energy that is often used to describe energy that is used over some period of time. A watt is a unit of power (amount of energy used over a given time period), defined as utilizing one joule of energy every second. A watt-hour is the amount of energy required to provide one watt of power over one hour of time. Since there are 3,600 seconds in an hour, one watt-hour equals 3,600 joules.

A British thermal unit (Btu or BTU) is the amount of energy that is needed (when added as heat) to raise the temperature of one pound of water by one degree Fahrenheit. The Btu is typically used (instead of the joule) in engineering calculations involving heating or cooling in the United States.

A separate unit in the English system of units is the foot-pound. It is defined in a similar manner as the joule, with one foot-pound being equal to the energy involved in moving with a force of one pound-force over a distance of one foot. However, the use of a pound-force can create confusion because the term “pound” is utilized to describe both mass and force in the English system of units. The foot-pound is used when mechanical energy (kinetic or potential energy) or work is involved.

Let us now use the above units to solve the first energy comparison question mentioned above: what takes more energy, lifting a 20-pound bag of potatoes from the floor to the kitchen counter or heating a small pot of water to boiling temperature?

Energy Comparison: Energy in the Kitchen

In the calculations of energy below, it is important to consider what quantity of energy is actually being calculated. In almost every process where there is a conversion of energy from one form to another, there is some inefficiency in the process. When lifting a bag of potatoes, some type of energy (if a person is doing the lifting, chemical energy in the form of glucose in the muscles or if a machine is doing the lifting, stored or produced electrical energy) is converted into potential energy as the bag is lifted up against the force of gravity.

The conversion of energy is never perfectly efficient. So when we talk about energy, we need to be careful and deliberate about what quantity we are actually measuring or calculating. Are we calculating the energy to perform a task in an ideal (imaginary) system or in the real world? The examples below will help to illustrate the difference.

So, what takes more energy, lifting a 20-pound bag of potatoes from the floor to the kitchen counter or heating a small pot of water to boiling temperature? First, we will determine the energy required to lift a 20-pound bag of potatoes to the kitchen counter.

As noted above, there is some inefficiency in the human body converting chemical energy stored in food to mechanical energy (work of physically lifting the bag of potatoes). In performing this energy calculation, we are ignoring that inefficiency and just considering the ideal (minimum) amount of energy to lift the bag of potatoes. That is, if the system for lifting the potatoes was perfectly efficient at converting stored energy into work to lift the bag of potatoes, how much energy would that system use?

Considered in this way, the energy required to lift the bag of potatoes is simply the difference in potential energy of the bag of potatoes between the countertop and the floor. The equation is: the difference in potential energy equals the mass multiplied by the acceleration of gravity multiplied by the change in height:

Let us first solve this equation using English units:

The result is 2,600 pounds-mass square feet per second squared. However, this unit is somewhat unwieldy. The more customary way to represent this amount of energy in the English system of units is using the unit of foot-pound. To understand how force and mass and mechanical energy are expressed in the English system of units, one would need to delve into the details of the units of the slug, pound-mass, and pound-force. Needless to say, it gets confusing. At any rate, expressed in foot-pounds, the energy would be 80 foot-pounds.

Now let us solve this equation using SI units:

A good approximation can be determined in this case without even using a calculator. Twenty pounds is approximately ten kilograms, and four feet is approximately a meter. The acceleration of gravity in SI units is about ten meters per second squared. So it is easy to calculate the energy in your head in this case and come up with about 100 joules, which would be pretty close to the right answer.

Now, we will determine the energy required to heat a small pot of water to boiling temperature. First, we need to make some assumptions. We will assume a “small pot” is about one liter (or 1.06 quarts) of water, and the temperature of the water is 50 degrees Fahrenheit (or 10 degrees Celsius).

Similarly in this calculation, there will be some loss of efficiency. If the heat source is a burner using a fuel (natural gas or propane), the gas will not burn perfectly, so there is still some chemical energy stored that is not converted to heat. With either a burner requiring fuel or an electric burner, not all of the heat will go into the water. Much of the heat is lost to the surrounding environment. Once again, for purposes of the calculation, we will assume we have a perfect system and no energy is lost in the conversion from chemical energy (fuel in a gas burner) or electrical energy (electric burner).

Thus, under the ideal system assumption, the energy required to heat the water is simply calculated as follows: heat energy equals specific heat capacity of the water multiplied by the mass of water multiplied by the change in temperature:

We will assume that the specific heat capacity of water is constant (even though in reality it varies with temperature), which is a pretty good assumption as it doesn’t change much in the temperature range we are looking at. First, using English units:

Since the definition of the British thermal unit was made for such problems, the calculation is fairly simple and the answer is 350 Btu’s.

Now, in SI units:

With the results from each calculation, we are ready to make some conclusions.

Conclusions

Hopefully, one of the first things you notice is that the energy involved in heating the pot of water (380,000 joules) is vastly greater than the energy involved in lifting up the bag of potatoes (110 joules). In fact, the potatoes would need to be lifted up to the countertop about 3,500 times to equal the amount of energy required to heat the pot of water. It sure is a good thing we have a burner to add that energy for us so we don’t have to add the energy mechanically. That would be a lot of lifting to get that water to boil!

Another item to notice is that we could immediately compare the values when we used SI units. The joule is an effective unit of energy when working with both mechanical energy and thermal energy. For the English units, however, we have two different units for the different kinds of energy. In order to compare the mechanical energy (80 foot-pounds) to the heat energy (350 Btu), you would need to know that there is a conversion factor of about 788 to convert foot-pounds to Btu’s. Thus, the 350 Btu’s is equivalent to 280,000 foot-pounds, which is a 3,500 times greater than 80 foot-pounds.

So, while using Btu’s or foot-pounds works just fine in some energy calculations, both of these units were made for specific kinds of energy and don’t easily relate to one another. I believe we are generally better off thinking about joules, an international standard that is easy to compare from one form of energy to another. The joule was designed to make sense as part of the overall SI system without getting messy and confusing like English units.

Another conclusion we can make is that while energy can be converted from one form to another, it is rarely very clean. There are always losses due to inefficiency. This is why experiments performed in the 1840’s to demonstrate the mechanical equivalent of heat (principally performed by James Prescott Joule) were so important and so revolutionary. The principle now known as conservation of energy (that energy is converted from one form to another such that energy is never lost in the process) was not obvious prior to those experiments. Energy is always “lost” in energy conversions, but it is never really lost in that it always goes somewhere.

Finally, as we already discovered, it takes a whole lot more energy to cook those potatoes than to get them up on the counter to prepare them. And not just by a little bit, but by a huge amount. This isn’t necessarily intuitive to us in daily life. But now you know the secret and are aware of the relatively enormous amount of energy required to change the temperature of water. So next time you are cooking on the stove, just think, that is a lot of energy going into that water!

Picture of potatoes in boiling water in a pot on the stove.

Kinetic Energy of Human-propelled Objects

Introduction

My goal with this post, as with many of my future posts, is to fill a hole in the Internet. That hole is readily accessible information about the kinetic energy of human-propelled objects.

You see, when I watch sports, I often think about physics. I think about energy and forces and friction and velocity. I’m not the only one that thinks about physics in connection with sports. In fact, physics of sports is getting to be big business these days. With professional sports being a multi-billion dollar industry, any possible advantage in competition is worth money. Sometimes science is utilized to help generate competitive advantages in sports. And on the other hand, teachers of physics all around the world have used sports for years to attempt to entice unsuspecting students into being interested in science. I found a great variety of web pages related to the physics of sports while researching for this post.

At any rate, one day while thinking about physics and sports, I thought of a question: what is the object that can be propelled by a human that has the most kinetic energy? There are various objects in sports that are propelled in various ways (thrown/ hit/ kicked/ rolled). What is the method that produces the most kinetic energy? What is the object that, when propelled, has the most kinetic energy?

After having this question, I performed an Internet search to find the answer. I couldn’t find it. I performed various searches, but was never successful in finding the answer. So I determined I would need to calculate the answer myself.

The math to calculate kinetic energy is not difficult. The equation is simply kinetic energy equals half of the value of the mass multiplied by the velocity squared.

So it becomes a matter of simply finding all the values and plugging them in to solve for kinetic energy. I selected a variety of possible winners for objects in sports and plugged in the numbers. The results are shown in the table below, sorted by most kinetic energy on top to the least kinetic energy on the bottom.

Results

First, I will discuss the results, and then make some disclaimers and notes about the data included. I do not include my sources for all of the numbers because the information is fairly readily verifiable except in a few cases as noted below. The first note I must add for consideration in discussing the results is that the numbers shown in the table are mostly maximum values. For example, the fastest speed for a human sprinting is about 12.3 meters per second, which represents Usain Bolt at his peak speed in an Olympic sprint event. This is obviously a lot faster than the average person can run. I applied the same rule to the different objects to find the fastest speeds they can go. So the average person will not achieve similar results to those shown in the table, and maybe not even close. But the maximum results give us a way to compare the different objects.

In looking at the results, the top entry is for a human sprinting, which I don’t consider to be in the category of “human-propelled object”. Thus, that entry is shown only for comparison purposes. Maximum kinetic energy of a human sprinting is approximately eight times the highest kinetic energy of a human-propelled object. This makes sense because when running, a person can continue to add energy to the “object” (their own body) as they pick up speed. The energy doesn’t need to be added all in one short burst as with any propelled object.

The rest of the results in the table were initially surprising to me, and perhaps are surprising to you as well. If I had thought about it some more and done some rough numbers in my head first, the results would not have been surprising (but sometimes one must simply calculate first and think later!). Let me explain. In the kinetic energy equation, the velocity is multiplied by itself while the mass is not. Thus, it would appear that the velocity of an object will be the dominant factor in determining total kinetic energy.

Thus, I figured a golf ball, which I knew must get to some pretty impressive speeds, would yield a high value for kinetic energy. A baseball also gets to relatively high velocities. As you can see, however, these are at the bottom of the table. It is the shot (which is the name of the spherical object that is “put” in a shot put try), with a relatively low velocity, that wins for the propelled object with the most kinetic energy. This is because the shot has a mass that is about 160 times that of the golf ball. While the golf ball does reach speeds five times higher than the shot (resulting in the velocity factor of the kinetic energy being 25 times greater), the shot’s overwhelming mass compared to the golf ball makes a greater difference in yielding a high kinetic energy value of about 750 joules.

The other Olympic throwing sports come right behind the shot put, with the discus around 600 joules and the javelin around 400 joules. A bowling ball, the first real object in the kinetic energy rankings that the average American sporting enthusiast has access to, comes next with about 350 joules. However, the bowling ball spends most of its time limited to rolling along the ground. Along with the preceding objects, the bowling ball is simply propelled into a field of play with no opportunity for further interaction by another player.

Thus, the soccer ball is the first object in the list that is actually “in play” during a sporting competition. That is, a soccer player has the opportunity to absorb the full impact of the almost 300 joules of kinetic energy of the soccer ball. Good thing soccer balls are relatively soft and have a large area of impact!

An arrow, at about 250 joules, and a bullet (typical 22 caliber rifle) at about 100 joules are included in the table for comparison. Obviously, the kinetic energy of a bullet depends significantly upon the type of weapon and bullet (as shown in a table on this blog post, which also includes the kinetic energies of some of the objects included here). However, it is interesting to consider that a soccer ball at high speed can have almost three times the kinetic energy of a typical 22 caliber rifle bullet!

Interestingly, a football and a baseball, when thrown at their respective highest speeds, have approximately the same kinetic energy at about 150 joules. While a football has approximately three times the mass of the baseball, the baseball can be thrown at speeds almost 70% faster than a football, resulting in approximately the same kinetic energy.

Further Discussion and Notes

When I first put the table together, I figured I would need to have separate categories for objects that utilize an external tool to be propelled (such as a golf ball, which is normally propelled by means of a golf club) and those that do not require an external tool, since I figured it would give objects an unfair advantage to have a tool to propel them. However, with the final results, it is clear that the winner, the shot, is an object that does not require an external tool.

One interesting find I had while researching the maximum speed of a football was this article about physics in football with some gross physics errors. The article mentions that the work done by a football quarterback is the force multiplied by the distance, which is approximately correct; however, the distance used in the article is the total distance traveled by the football instead of the distance that should have been used, that traveled by the football during the quarterback’s arm motion. Thus, the work done on the football is calculated at 67,000 joules instead of about 150 joules as it should have been (incidentally, the value used for the force applied is also incorrect), as the work done on the football should approximately equal the kinetic energy of the football as it leaves the quarterback’s hand. This just goes to show you can’t trust everything you read about physics on the Internet.

For baseball, you might wonder if balls can be batted faster than they are pitched. The answer is yes. The maximum speed of a batted ball can get upwards of 120 miles per hour (compared to maximum pitch speed of 100 mph). The forces involved in the collision of baseball to bat can be pretty spectacular, as explained in an article from Popular Mechanics.

It was somewhat difficult to find the maximum speed of a shot put. I ended up just using the world record shot put distance and the fact that a typical shot put launch angle is 40 degrees to solve for shot put speed. There is a related physics homework problem (with fictional data), but the result is that the equation to solve for velocity is:

This yielded a velocity of 14.4 meters per second, which makes sense with a related article that solves for a female Olympic athlete’s shot put speed at 13.5 meters per second.

An athlete putting some serious kinetic energy into a shot (the round metal ball)!

One object I considered including was an atlatl, but I found it to be not significantly different from an arrow. I thought perhaps hunters before firearms were available would have found a way to get a lot of kinetic energy into an object for survival purposes, but it appears that maximum kinetic energy is not the only consideration in launching a projectile for hunting purposes.

Another object I considered including was a curling stone. However, the speeds of curling stones in competition are so low (two to three meters per second) that the kinetic energy ends up being pretty low as well. I suspect with the right conditions, an athlete could find a way to propel a curling stone at significantly higher rates of speed. Since a stone has a mass of about 18 kilograms (about 40 pounds), the kinetic energy could get pretty high.

I learned a few things about archery. Increasingly sophisticated compound bows have been consistently topping previous arrow speed records in recent years. Also, there is a lot of thought put into the mass of an arrow, and the experts have a lot to say about that. Thus, it is difficult to come up with a good “average” number for arrow mass, but I put what I thought was reasonable based on my research.

Another interesting tidbit I found was that the javelin was redesigned in 1986 to keep throwing distances down. The world record had gotten over 100 meters, which was unsafe for some competitions. I just found it interesting that the record distance was intentionally limited when the usual purpose of Olympic competition is to showcase maximum human abilities.

In calculating the kinetic energy of the various objects, I have neglected rotational kinetic energy. Some objects have a significant amount of spin on them, such as a golf ball with up to 2000 rpm and a baseball with up to 1800 rpm. I won’t go further into that realm in this post, but it may be something to explore in a future post.

Conclusion

So the winner is the shot of the shot put event! So if anyone ever tells you they will give you a dollar for each joule of kinetic energy you can produce by propelling some sports-related object with your own power (I know, this happens to me all the time, too), the shot put is a good choice. You might want to practice your form so you will be ready. And if that circumstance never happens, I hope you enjoyed reading this post and considering the energy of human-propelled objects anyway.

If you are interested, here is the spreadsheet for calculating the kinetic energy of the various objects. You can expand to include your own objects if you want. Let me know what you discover!

Kinetic Energy of Human-propelled ObjectsDownload

Introduction

In full recognition that I am stating the obvious, this is the first post on this blog. Thus, it behooves me to outline the intentions and purpose of the writings herein. It is my intent in this post to describe what this blog is and what it is not.

Let me start by explaining my passion for energy. I have, as far back as I can remember, always loved the topic of energy. Energy, considered broadly, is behind the scenes for every process on the earth and in the universe, small and large. Energy comes in various forms. I have an interest in all the various forms of energy, and in the conversions between the forms, which include: mechanical energy (kinetic and potential), thermal energy, electrical energy, chemical energy, nuclear energy, and even dark energy. All of these I intend to explore further in future posts.

Perhaps the most famous scientific equation in the world today (that is, the most popular answer when randomly asking someone to state any scientific equation) is E equals M C squared:

meaning energy equals mass times the speed of light squared. This expression identifies the equivalency between energy and mass. Its popularity gives an indication that energy is a concept that is recognized as important in society as a whole, though not everyone completely understands it. In fact, I would argue that no one completely understands the concept of equivalency between mass and energy, myself definitely included.

At any rate, partly because of my interest in energy and the desire to understand the complex workings of energy in the universe, I pursued and eventually acquired a bachelor’s degree in physics. I also obtained a master’s degree in nuclear engineering and have put those degrees to good use working in a career in engineering.

I have been inspired by various scientists, engineers, and writers along the way. Besides the famous, recognizable ones and the lesser known ones that I have known personally, three figures inspirational to this particular blog are Vaclav Smil, Steven Levitt, and Stephen J. Dubner (the latter two of the Freakonomics team). I will borrow something of the writing and thinking style of these three for this blog.

So what do I intend to include about energy in this blog? What will be my topic of particular focus? How will I narrow down this vast topic into something worth reading? Well, I do not intend to limit myself. If a topic somehow relates to energy, I will include it. I may cover anything and everything about energy. This includes not only scientifically measurable energy (which is what I will devote most of my attention to) but also metaphysical (I hope I am not abusing that word too much) forms of energy (as in, “I just don’t have the energy for that now”, meaning not “I do not have the necessary stores of chemical energy in my body tissues to do that”, but rather “that is outside what I feel capable of accomplishing at this moment”).

Now, I realize that not everyone shares my passion for energy, and most people probably don’t think about it as much as I do. So how is anyone else going to get anything out of this blog? Well, it is my goal to write in an engaging style that anyone can appreciate. I will have some technical concepts and some equations and math in here, but if you don’t want those details, just skip over that part. I really enjoy taking concepts that may be technical and difficult to understand and breaking them down to where anyone can understand them. It is my plan to include charts and tables in this blog to make things more interesting and easy to understand.

The purpose of this blog is to fulfill its broad and overly vague title of “Thoughts on Energy”. I decided that was a fitting title for my intended subject for writing, energy in just about any context. When one performs an Internet search for “thoughts on energy”, the most popular results that come up are related to the (hypothesized) relationship between thoughts and energy. I don’t mean to connect the two as the main topic of my blog. That is, this isn’t a blog about how thoughts and energy are related. No, this is just a blog with my thoughts about the topic of energy.

I recognize that there are many ways to produce and absorb content these days, from audio messages (podcasts and audiobooks) to video (Youtube) to various forms of the written word. I have obviously chosen as my medium the written word. My goal is to produce content that is interesting to read and includes relevant links so that the reader can find additional information on a particular topic if they so desire. I also intend to make the content audio-friendly such that someone can listen to the content as well and benefit from it. I know I enjoy listening to a good TED talk on my commute to and from work. Perhaps someday I will branch out into other forms of content such as Youtube videos, but for now I am going to explore writing.

For most of the rest of this post I will explain the guiding principles behind my writing, which you may or may not care about. Feel free to skip to the next post at this point if you have had your fill of introductory remarks. The guiding principles, which I will explain further below, are:

  • Transparency
  • Accuracy
  • Relevancy
  • Thoroughness
  • Agreeableness

First, transparency. I do not have a hidden agenda, and it is never my intent to misconstrue data. I intend to be open about where I am getting my facts and am always open to being corrected. I reserve the right to be smarter tomorrow than I am today. I will probably never claim to have the final answer on any particular topic. This blog is exploratory, not authoritative.

Second, accuracy. Notwithstanding the transparency ideal in the previous paragraph and the resulting constant possibility of being corrected by new and better data, my goal is to be as accurate as possible. I want to provide content you can trust. However, obviously I can’t be an expert in every subject, and thus I may misstate some things. I might make math mistakes every once in a while (I doubt it, but it is possible).

Next, relevancy. In this blog I will provide fresh, relevant, and thought-provoking content. It is natural that content published on the Internet can have a short shelf life. What is relevant today (be it sports, pop culture, or other news) is often stale and inconsequential in the future (though they may still have some significance as historical interest). My goal is to produce content that is general enough that it will be relevant far into the future, so that when this content is found years from now it can still be interesting and useful. Also, my intent is that the content will be useful for pretty much anyone that can read. The content will be understandable by the average educated person (usually including middle and high school students) and yet still stimulating and interesting to the more advanced scientists, engineers, and mathematicians out there who have an interest in energy-related topics.

The next guiding principle is thoroughness. In reality, I wasn’t even sure that was a word until I typed it out and my word processor seems to be okay with it. What I mean is that I intend to be complete in my treatment of a topic. This is dangerous, of course, because if I attempt to be too complete, these posts will get way too long, and too long is easily ignored and thus not effective in reaching people. Thus, I will limit myself to adequate treatment of a topic and always reserve the right to bring up the topic (or a closely related topic) again in a future post. Of course I can’t be fully thorough on any topic. There are entire books and entire research careers devoted to many of the topics I intend to treat. My purpose is not to be the most definitive source in every energy topic, but to present some ideas in a broad sense for further consideration.

The last guiding principle to expound upon is agreeableness. By this I mean that I do not intend to produce any controversial material. I will stay away from politics. I do not intend to get anyone riled up. I will not intentionally write anything offensive to any particular individuals or groups.

Thus concludes my guiding principles. On a related note, I don’t intend to produce any material meant to be popular for popularity’s sake. Certainly, I would appreciate a large audience of people partaking of the content I produce and finding it to be worthwhile, but it is not my intention to seek wide acclaim for my writing. I will maintain freedom to write according to my interest and not according to what will generate the most traffic. In my opinion, too much of the content of the Internet has degraded into a contest of excessive sensationalism. Thoughtful dialogue has in many cases been replaced by “click bait” designed to elicit just enough curiosity to entice someone to click on a link, and then not provide any meaningful content. But I digress.

Next, no introduction is complete without a few disclaimers. I don’t provide any investment or tax advice in this blog. I also don’t provide relationship or psychiatric advice. I’m not a doctor. I don’t have access to secret archives or millions of dollars of research funding or special equipment. I’m just one guy with a computer and access to the Internet and a lot of passion for energy and for writing, but I think that is pretty powerful by itself.

Finally, is this really the blog you should be reading if you have an interest in energy? Maybe there is a similar blog out there that is better than this one. Certainly this type of thing has been created before. Honestly, there probably is a better blog out there for whatever you are looking for, and I hope you find it. In the meantime, I hope you will enjoy this blog.

Also, I personally couldn’t find anything similar to what I intend this blog to become; that is part of why I decided to create it. Sure, there are lots of energy blogs out there. An Internet search of the term “energy blog” yields a lot of results, but they seem to be either narrow in focus or industry-centric, that is, focused on energy as an industry and not energy for its own sake.

Some of the notable blogs I found include Energy Central dot com, which seems to have a good balance of various energy industry news items, Your Energy Blog dot com, which has a pretty good mix of content but hasn’t been updated for a few years and appears to overemphasize the sensational, and Renewable Energy World dot com, which is, as the name implies, narrowly focused on renewable energy.

But perhaps it is too much to ask of an Internet search to find something like the blog I intend to create using as broad a search as “energy blog”. Perhaps a search of the term “random thoughts about energy” would yield better results. I can tell you from my experience that that search does not yield better results. The first result in my search was a blog from someone in Australia who seems to focus these days on criticism of the government, but the blog overall seems to focus on religious content. The next result is a person in the United Kingdom focused on energy policy and that seems to be pretty boring. Other notable results include one from a gentleman in the United Kingdom who seems to have something similar to what I want, but only has four posts that appear to be pretty old. Finally, there is a blog from a gentleman in California, but it is very narrow related to energy (electricity) markets, and is heavy enough in policy that most normal people (including me) probably can’t read much of it.

So, if you find a blog out there similar to this one, let me know. I personally think this blog is pretty special. But I may be biased.

With the introduction now complete, let us get to the real content!