Professor Susskind derives the formula for the pressure of an ideal gas. He begins by introducing the Helmholtz free energy, and the concept of adiabatic processes. These concepts lead to the definition of pressure as the change of energy with volume at a fixed entropy, and then to the famous equation of state for an ideal gas: pV = NkT.
Professor Susskind then moves on to define the concept of fluctuations., and in the process demonstrates once again that the power in statistical mechanics lies in the partition function and is derivatives. The fluctuation of energy in a system leads to the definition of the heat capacity of the system and the specific heat of a given material.