Thermodynamics Ques 23
23. 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
[2004]
(a) $(T-4) K$
(b) $(T+2.4) K$
(c) $(T-2.4) K$
(d) $(T+4) K$
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Answer:
Correct Answer: 23.(a)
Solution:
- (a) $T_1=T, W=6 R$ joules, $\gamma=\frac{5}{3}$
$ \begin{aligned} W & =\frac{P_1 V_1-P_2 V_2}{\gamma-1}=\frac{n R T_1-n R T_2}{\gamma-1} \\ & =\frac{n R(T_1-T_2)}{\gamma-1} \end{aligned} $
$n=1, T_1=T \Rightarrow \frac{R(T-T_2)}{5 / 3-1}=6 R$
$\Rightarrow T_2=(T-4) K$
BETA
