Toast and Cocoa

Imagine that you have been out playing in the snow, or ice skating on a frozen pond. You come in from the cold and your mother offers you a choice of either a stack of hot toast or some warm cocoa. Which would you choose to warm you up?

Most of us would choose the cocoa. The reason behind this is based on two related ideas. The first is that when two things at different temperatures are in contact, heat transfers from the warmer object to the cooler one until their temperatures are the same. In this case, that means that anything you eat or drink will end up at body temperature. Hot toast will give heat to your body until it reaches body temperature (about 37 oC). Likewise, cocoa will give heat to your body until it, too, reaches body temperature.

The other related idea is that different things require different amounts of heat to change their temperatures. If you leave a stack of hot toast on the kitchen counter for a few minutes, it will quickly cool to approximately room temperature. A cup of cocoa, however, will still be quite warm after sitting on the same counter for the same amount of time. This is NOT because the temperature change for the cocoa is greater, in fact, it is LESS than that of the toast. The difference is the amount of heat that must be removed from toast to change its temperature is much less than the amount of heat that must be removed from cocoa to make the same change in temperature.

Putting these two ideas together is relatively straightforward. Both the toast and the cocoa will give heat to your body until they reach body temperature, but the cocoa needs to give away more heat to undergo that temperature change. Since your body is taking that heat, cocoa will give you more heat and therefore do a better job of warming you than the toast will.

This idea, that some things must give away more heat than others when cooling down is called heat capacity.
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