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One mole of an ideal gas at an initial temperature of T K does 6R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be:

1. (T − 4) K
2. (T + 2.4) K
3. (T − 2.4) K
4. (T + 4) K

Correct answer: (T − 2.4) K

Solution

In an adiabatic process, the work done is related to the temperature change by the first law of thermodynamics. Using the relation W = (nCvΔT) and the given γ = 5/3, we calculate the final temperature as T_final = T - 2.4 K.

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