Both volume and entropy serve as (*) natural variables for this quantity, and the derivative of this quantity with respect to temperature at a constant volume gives the heat capacity.
For a Fermi gas, this quantity is equal to three-fifths times the number of fermions times epsilon sub F. In the Debye model, this quantity is equal to the product of h-bar, frequency, density of states, and the Bose-Einstein factor, integrated over all frequencies. For a single particle in a gas, this quantity is equal to thermal pressure over density times one over quantity adiabatic index minus 1. Taking a Legendre transform of this quantity gives the Helmholtz free energy. Both volume and entropy serve as (*) natural variables for this quantity, and the derivative of this quantity with respect to temperature at a constant volume gives the heat capacity. This quantity plus the product of pressure and volume gives the enthalpy, and this quantity is constant for an isolated system. For 10 points, name this quantity, whose change is equal to the sum of the heat transfer to a system and work done on the system according to the first law of thermodynamics.
For a Fermi gas, this quantity is equal to three-fifths times the number of fermions times epsilon sub F.
internal energy [or U]