Below it is proved that the internal energy of an ideal gas depends only on its temperature. Therefore,
and therefore The process is adiabatic, so from the first law of thermodynamics which implies that Using integration by parts then gives that is constant. Therefore, answer (C) is correct. Proof that the internal energy of an ideal gas depends only on its temperature: implies that implies that From and the equality of mixed partial derivatives it follows that Therefore, equation 1 becomes which equals for an ideal gas. This completes the proof. |

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