During an adiabatic process, one finds that nCvdT+pdV = 0. (12) Once we replace the p with its equivalent state from the ideal gas law, a relationship appears between temperature and volume. Integrate the equation for finite changes to get a natural-log solution of T and V that adds to 0.

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To derive the relationship between temperature and volume for an adiabatic process of an ideal gas w... View the full answer