Heat Engines and the Second Law of Thermodynamics for AP Physics B

Practice problems for these concepts can be found at:

Thermodynamics Practice Problems for AP Physics B

The second law of thermodynamics is less mathematical than the first law, and it is also probably more powerful. One of many ways to state this law says.

Pretty simple, no? Heat engines and their cousins, refrigerators, work by this principle. Figure 18.6 shows what a heat engine looks like to a physicist.

In a heat engine, you start with something hot. Heat must flow from hot stuff to cold stuff … some of this flowing heat is used to do work. The rest of the input heat flows into the cold stuff as exhaust. A car engine is a heat engine: you start with hot gas in a cylinder, that hot gas expands to push a piston (it does work), and you're left with colder² exhaust gas.

We define the efficiency of a heat engine by the ratio of the useful work done by the engine divided by the amount of heat that was put in. This is stated by the following equation:

The efficiency, e, of an engine is always less than 1. If the efficiency of an engine were equal to 1, then all the heat in the hot stuff would be turned into work, and you'd be left with material at absolute zero. That's tough to do, so we'll settle for an efficiency less than 1.

Since all heat engines operate at less than 100% efficiency, it is useful to calculate what the maximum possible efficiency might be, assuming the engine is as well made as possible to eliminate energy losses to friction, insufficient insulation, and other engineering concerns. It is found that this ideal efficiency for a heat engine depends only on the temperatures of the hot and cold reservoirs.

T_H is the temperature of the hot stuff you start with, and T_C is the temperature of the colder exhaust. These temperatures need to be measured in kelvins.³

Just because a heat engine is "ideal" doesn't mean its efficiency is 1. The same argument we used above still applies: efficiency is always less than 1. And real, nonideal engines operate at only a fraction of their ideal efficiency.

A refrigerator is like the backward cousin of a heat engine. Physicists draw a refrigerator as shown in Figure 18.7.⁴

In a refrigerator, work is done in order to allow heat to flow from cold stuff to hot stuff. This sounds like a violation of the second law of thermodynamics. It isn't, though, because the work that is done to the system must have been the product of some sort of heat engine. Heat will not spontaneously flow from cold stuff to hot stuff; it is necessary to do net work on a gas to get heat to flow this way.

By the way: the behavior of a heat engine can be represented on a PV diagram by a closed cycle. If the cycle is clockwise, you're looking at a heat engine, and the net work per cycle is negative (done by the gas); if the cycle is counterclockwise, you're looking at a refrigerator, and the net work per cycle is positive (done on the gas).

Entropy

Entropy is a measure of disorder. A neat, organized room has low entropy … the same room after your three-year-old brother plays "tornado!" in it has higher entropy.

There are quantitative measures of entropy, but these are not important for the AP exam. What you do need to know is that entropy relates directly to the second law of thermodynamics. In fact, we can restate the second law of thermodynamics as follows.

This means that the universe moves from order to disorder, not the other way around. For example: A ball of putty can fall from a height and splat on the floor, converting potential energy to kinetic energy and then to heat—the ball warms up a bit. Now, while it is not against the laws of conservation of energy for the putty to convert some of that heat back into kinetic energy and fly back up to where it started from. Does this ever happen? Um, no. The molecules in the putty after hitting the ground were put in a more disordered state. The second law of thermodynamics does not allow the putty's molecules to become more ordered.

Or, a glass can fall off a shelf and break. But in order to put the glass back together—to decrease the glass's entropy—someone has to do work.

Practice problems for these concepts can be found at:

Thermodynamics Practice Problems for AP Physics B