The Entropy of an Ideal Gas We use the relation σ = - to find the entropy from the free energy. Without much work, we come up with: σ = N log + The Energy of an Ideal Gas Remember that the free energy can be defined in terms of the energy as follows: F = U- τσ . We rearrange to solve for U , and plug in our values for F and σ to find the simple result: U = Nτ The Heat Capacity of an Ideal Gas A measure of how much heat a gas can hold is the heat capacity. There are two slightly different measures of the heat capacity. One, the heat capacity at constant volume, is defined as C V âÉá . The other, the heat capacity at constant pressure, is defined as C p âÉá . The only difference between the two definitions is in what is held constant in the derivative. The results for an ideal gas can be obtained by direct substitution and differentiation for the heat capacity at constant volume, and by the thermodynamic identity for the heat capacity at constant pressure. The results are:
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