Enthalpy

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Enthalpy of the monatomic ideal gas

The internal energy of the monatomic ideal gas is given by

U_{m} = \frac{3}{2} R. T + U_{m, 0} .

For the enthalpy it follows with the ideal gas law

H_{m} = U_{m} + p V_{m} = U_{m} + R. T = \frac{5}{2} R. T + U_{m, 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} = {(\frac{\partial H_{m}}{\partial T})}_{p} = \frac{5}{2} R.

which results in the difference in the molar heat capacities

{C.}_{p, m} - {C.}_{V, m} = \frac{5}{2} R. - \frac{3}{2} R. = R.

Always there for ideal gases $p V_{m} = R. T$ 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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