Suppose that you have some air in a metal cylinder with a sliding piston lid. Imagine that no air can leak around the tight-fitting edges of this lid.
You now wish to raise the temperature of this air by, say, 28 K. One way to do this is to place the cylinder on a hot plate so that heat will flow from the high-temperature plate through the metal to the lower-temperature air inside. Let's suppose that it takes 430 J of added heat to raise the temperature by the desired amount.
Another way to accomplish the same thing without any heat flow would be to compress the air: By pushing the lid inward, we exert a force on air molecules within and move them in the direction of that force. In other words, we do work on the air by compressing it. How much work would it take to make the temperature rise by 28 K? Experiments tell us that it would take the same 430 J as before.
In fact, we find in the lab that there are many ways to bring about this change in the air's thermal state:
add 150 J of heat while also doing 280 J of work
add 560 J of heat, then do -130 J of work (i.e., let the air in the cylinder expand and do +130 J of work on the air outside)
do 690 J of work, then immerse the cylinder in cold water and add -260 J of heat (i.e., allow +260 J of heat to flow out of the cylinder into the lower-temperature water)
In each of these cases the sum of heat added to the air plus work done on the air is 430 J. We say that we're increasing the air's internal energy (a.k.a. thermal energy) by 430 J, and that this can be accomplished by adding heat to the air, doing work on the air, or any combination of the two. Here's a second example: You can melt ice by heating it, or you can melt it by compressing it under the blade of your ice skate. (This is why snow doesn't crunch under your feet unless it's incredibly cold outside: You melt some of it as you step on it.)
Let's sum this up. For any physical system we're interested in -- a cylinder of air, a bucket of water, anything -- we can write the following equation:
(change in system's internal energy) = (heat added to system) + (work done on system)
This statement is the First Law of Thermodynamics, which is essentially the law of conservation of energy, updated (in the mid-1800s) to acknowledge that heat flow is a form of energy transfer. (Prior to that, heat was thought to be a material -- an invisible fluid called "caloric" -- rather than added or subtracted energy.) If you tell me what change you want to make in a system -- temperature rise, pressure increase, melting, chemical reactions, etc. -- I can tell you how much internal energy will have to be added or taken away, but I can't tell you how much work it will take or how much heat it will take, for there's an infinity of possibilities.
(Nor can I tell you how much heat is "in" the system, any more than I could tell you how much rain is in a certain lake. Any water in the lake could result from rain or springs or feeder streams, and I can't separate them out; any internal energy in a system could result from heat added or work performed, and I can't separate them out. I could tell you how much water is in the lake or how much internal energy the system has; I also could tell you what volume of rain was added during the last 24 hours, or how much heat was added to the system during the last five minutes. Moral: Heat is not synonymous with thermal energy and internal energy.)
By the way, your car engine has four, six, or eight metal cylinders with tight-fitting piston lids and air (mixed with a bit of gasoline vapor) inside. We'll see later on that the engine cycle is a series of work increments and heat increments that add up to zero net change in internal energy. But this is useful, for the net effect is that a large amount of thermal energy is added (through combustion), allowing the air to do a fair amount of work (pushing the piston outward) and to lose the rest of the added thermal energy as heat flow (warming up the coolant fluid).
The First Law of Thermodynamics
Written by Chris Magri
Last modified on August 29, 2016
URL: https://sites.google.com/a/maine.edu/magri/phy110c/firstlaw