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This Halloween, when you grab a candy bar, pay attention to the wrapper. In the United States, a "nutrition facts" label has been required for all packaged foods since 1994, giving the serving size and the amount of sugar, protein, fat, and sodium the food contains. But the most interesting bit is the metric for energy, which is listed as "calories." What does energy really mean when it comes to candy?
Flavors of Energy
In physics, the concept of energy helps us keep track of different types of interactions. We say energy is “conserved” for all interactions, meaning that if you calculate the total energy before and after something happens, that value will be constant.
During these interactions, energy can change from one type to another. I like to think of these types as “flavors” of energy. There's the energy of a moving object, a flavor we call kinetic energy. There's energy stored in the gravitational field, a flavor we call gravitational potential energy. There's energy stored in the interaction between two charged particles, or electric potential energy. And of course when things get hot, there's an increase in thermal energy.
All types of energy are interchangeable. How do you change energy from one flavor to another? I mean, we do this every day when we brew a pot of coffee. When current—electrical energy—runs through a wire, that wire gets hot. You can use this heat to increase the temperature of water. (That’s thermal energy.) We can calculate the electrical energy by measuring the electrical current and voltage across the wire. This will be equal to the change in the thermal energy of the water.
There's also a connection between mechanical energy and thermal energy. Imagine that you have a tank of water and you want to use some spinning paddles to stir it. Your paddle system has three parts: the paddles at the bottom, a length of rope in the middle, and a heavy weight that slides along the rope from top to bottom. As gravity pulls the weight down along the rope, the paddles spin and push the water. This causes the water to move, but the frictional interaction also heats the water up. The change in the gravitational potential energy of the weight as it moves down the rope is equal to the change in thermal energy of the water. Energy from motion has turned into heat energy.
The Joule, the Calorie, and the (Other) Calorie
In physics, our preferred unit for energy is the joule. Historically, the value of 1 joule could be defined as the energy that a force of 1 newton produces when moved 1 meter. A joule is also equal to the electrical energy from a current of 1 amp and voltage of 1 volt for one second.
It can be difficult to get a feel for this unit, so try this simple experiment: Take a textbook and put it on the floor. Now pick it up and put it on a table. Since the book moved up, it gained more gravitational potential energy. The energy increase is approximately 10 joules. (The actual value depends on the height of the table and the mass of the book.)
The calorie is another unit of energy. It comes from the thermodynamic side of energy, so it has to do with changes in temperature. The value of a calorie is equal to the energy required to raise 1 gram of water by 1 degree Celsius.
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Of course, energy is still energy. If you use an electrical current to heat 1 gram of water by 1 degree C, it would take 4.184 joules. So a calorie is equal to 4.184 joules—there's your unit conversion.
Let's say a candy bar’s packaging says it has 200 calories. That seems like a reasonable value, but I have some bad news for you. A candy bar actually has 200,000 calories, not 200. The metrics on food packages are given in kilocalories, so it's actually one-thousandth of the energy the food contains. To prevent confusion, we sometimes call these "food calories," as distinct from “chemistry calories.” Other people capitalize “Calorie” to signify the food version.
Now let’s say you wanted to work off the 200,000 calories in this candy bar by doing pull-ups. With each pull-up, your muscles use energy to lift your body and increase your gravitational potential energy. Using a rough estimate of a body mass of 70 kilograms and a lift height of 60 centimeters, we get a change in energy of about 412 joules (right around 100 chemistry calories, or just a 10th of a food calorie) to do each pull-up.
Of course, the human body isn’t perfectly efficient, so it takes much more food energy to pull up your weight. If you assume an efficiency of 10 percent, then a person would actually burn about 1,000 chemistry calories per pull-up. That means you would need to do 200 pull-ups to make up for the 200,000 calories in that one candy bar. Is that worth it? Maybe it is.
How to Measure the Energy in a Candy Bar
Suppose I make a brand-new physics-based candy bar called the Newton Nougat Crunch. Before it goes on the market, I need to determine how many calories it contains. One way to measure the energy content in food is with a bomb calorimeter. Yes, that is a real thing. Here's a picture of an older version of this device. (I like the older ones—they have more character.)
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On the right is a metal container. This is the bomb part—the device itself doesn't explode, but it does combust whatever’s inside of it. Inside this canister, I will place a small piece of the new candy bar. If I can find the energy contained in just this small part, then I can extrapolate to find the total energy.
The bomb is then sealed and filled with oxygen. An ignition source starts a combustion reaction with the oxygen, essentially burning the candy. Of course, this reaction gets hot. Now if I can measure the change in thermal energy of the reaction, I can calculate the amount of energy in the candy.
To measure this change in thermal energy, I put the bomb in a bath of water. After the reaction, both the bomb and the water will increase in temperature, which can be measured with a thermometer. If you know the thermal properties of water (we do) and of the metal bomb container (again, yes), then the change in temperature can be used to calculate the change in thermal energy. That energy is the energy contained in the little bit of candy. Convert that to weird food calorie units, and that’s how you get the value that goes on the package.
Let’s say heating up a gram-sized piece of Newton Nougat Crunch raises 2 kilograms of water by 1 degree Celsius. That means that each 1-gram piece of Newton Nougat Crunch is 2 kilocalories. If the whole candy bar is 50 grams, then it will contain 100 food calories. (That’s pretty low for a real candy bar, but this is special physics candy.)
There's actually another way to get this calorie measurement. If you know the calorie values of all the ingredients—like the amount of sugar and milk and whatever else goes into it—you can just calculate the total based on the amount of each ingredient you used. Personally, I think the bomb calorimeter is cooler.
