The first part of this chapter computes the entropy of an ideal gas. This is a fairly complex calculation, and we won't consider it further. Instead, we will investigate the consequences of the resulting formula for the entropy.
The temperature of an ideal gas is computed in the usual way, except that you have to remember to hold the volume constant when taking the derivative of entropy with respect to energy.
The ideal gas is different from the brick in that the entropy depends on the volume as well as the energy. The pressure of an ideal gas is minus the derivative of the energy with respect to volume, holding entropy constant. This obtains the pressure as a function of energy and volume. Eliminating energy in favor of temperature yields the ideal gas law.
The important results for the ideal gas are (a) the ideal gas law, (b) the energy as a function of temperature, and (c) the energy as a function of volume and entropy.
There are two different specific heats for a gas, specific heat at constant volume and constant pressure. The one used depends on the process of interest.
There is a big difference between slow and rapid expansions and compressions of a gas. Be sure to understand this difference.
A heat engine is a device which takes heat from a high temperature reservoir, converts part of this to useful energy, and deposits the rest in a low temperature reservoir. The fraction of this heat which can be converted to useful energy is a function only of the ratio of temperatures of the two reservoirs. A device which purported to extract a larger fraction as useful energy would violate the second law of thermodynamics and is called a ``perpetual motion machine of the second kind''.
It is easy to determine the efficiency of a cyclic process using a plot in the energy-entropy plane. A process which traces a rectangular path in this plane is called a ``Carnot cycle''.
A refrigerator is a heat engine running backwards.