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  4. 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, then final temperature of the gas will be :

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Q. 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, then final temperature of the gas will be :

WBJEEWBJEE 2006

Solution:

Work done by gas in adiabatic process $ W=\frac{nR({{T}_{i}}-{{T}_{f}})}{\gamma -1} $ $ \therefore $ $ 6R=\frac{1\times R(T-{{T}_{2}})}{{{(5/3)}^{-1}}} $ or $ 6=\frac{T-{{T}_{2}}}{2/3} $ or $ T-{{T}_{2}}=4 $ $ {{T}_{2}}=(T-4)k $