One mole of an ideal gas at an initial temperature of $T~ K$ does $6~ R$ joules of work adiabatically. If…
One mole of an ideal gas at an initial temperature of $T~ K$ does $6~ R$ 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:
$(T+2.4) K$
$(T-2.4) K$
$(T+4) K$
$(T-4) K$
Solution
We know that work done in adiabatic process is:
$\begin{aligned}
& W=\frac{-1}{V-1}\left(P_f V_f-P_i V_i\right) \\
& \Rightarrow \quad 6 R=\frac{-1}{\frac{5}{3}-1}\left(T_f-T_i\right) \\
& \text { Since } P V=R T\} \\
& \Rightarrow \quad T_f-T_i=-4 \\
& \Rightarrow \quad T_f=(T-4) \mathrm{K} \\
&
\end{aligned}$
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