For any gas whose equation of state is given exactly by pV = nRT (or pv = RT), the specific internal energy depends on temperature only. This rule was originally found in 1843 by an English physicist James Prescott Joule experimentally for real gases and is known as Joule’s second law:
The internal energy of a fixed mass of an ideal gas depends only on its temperature (not pressure or volume).
The specific enthalpy of a gas described by pV = nRT also depends on temperature only. Note that enthalpy is the thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume. In intensive variables the Joule’s second law is therefore given by h = h(T) = u(T) + pv = u(T) + RT.
These three equations constitute the ideal gas model, summarized as follows:
pv = RT
u = u(T)
h = h(T) = u(T) + RT