The specific heats are particularly useful for thermodynamic calculations involving the ideal gas model.
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:The ideal gas model assumes that the gas molecules don't interact with each other.
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The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important.
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:: In particular, look at the assumption about the actual volume occupied by the gas molecules that is built into the ideal gas model.
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The ideal gas model has been explored in both the Newtonian dynamics ( as in " kinetic theory " ) and in quantum mechanics ( as a " gas in a box " ).
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In particular, the short average distances between molecules increases intermolecular forces between gas molecules enough to substantially change the pressure exerted by them, an effect not included in the ideal gas model.
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The ideal gas model has also been used to model the behavior of electrons in a metal ( in the Drude model and the free electron model ), and it is one of the most important models in statistical mechanics.
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