Question

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 $\frac{5}{3}$, the final temperature of gas will be :-

• A. $(T-2.4)K$
• B. $(T+4)K$
• C. $(T-4)K$
• D. $(T+2.4)K$

Answer 1

Answer: (C)

$(T-4)K$

$\Delta =\mu C_v\Delta T$ and $0=W+\Delta U$

$\Rightarrow \Delta U$ = $-6R(\therefore W=6R)$

Therefore $-6R=1\left(\frac{R}{\gamma -1}\right)\Delta T=\frac{3}{2}R\Delta T$

$\Delta T=-4\Rightarrow T_{final}=(T-4)K$

So, the correct option is $C$