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## Enthalpy of the monatomic ideal gas

The internal energy of the monatomic ideal gas is given by

$Um=32R.T+Um,0.$

For the enthalpy it follows with the ideal gas law

$Hm=Um+pVm=Um+R.T=52R.T+Um,0.$

As expected, the enthalpy is independent of the pressure for the ideal gas. For the molar heat capacity at constant pressure, the derivation of Eq. (2) after $T$

$C.p, m=∂Hm∂Tp=52R.$

which results in the difference in the molar heat capacities

$C.p, m-C.V, m=52R.-32R.=R.$

Always there for ideal gases$pVm=R.T$ applies, shows here as with the internal energy of ideal gases but in a different way that the difference $C.p, m-C.V, m$ for any particle always equal to the gas constant $R.$ is as far as the gas shows ideal behavior.

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