done by the system is defined as

However, does not remain constant during an adiabatic process but instead changes along with .

It is desired to know how the values of and relate to each other as the adiabatic process proceeds. For an ideal gas (recall ideal gas law the internal energy is given by

where is the number of degrees of freedom divided by 2, is the universal gas constant and is the number of moles in the system (a constant).

Differentiating equation

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