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  4. One mole of an ideal gas at an initial temperature of TK 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

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Q. One mole of an ideal gas at an initial temperature of $TK$ 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

NTA AbhyasNTA Abhyas 2020

Solution:

$W=\frac{R \left(T_{i} - T_{f}\right)}{\gamma - 1}\Rightarrow 6R=\frac{R \left(T - T_{f}\right)}{\left(\frac{5}{3} - 1\right)}\Rightarrow T_{f}=\left(\right.T-4\left.\right)K$