Question

$1mole$ of an ideal gas at an initial temperature of $TK$ does $6R$ joule 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

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

Answer 1

Answer: (A)

$(T-4)K$

We have, specific heat ratio $=\gamma =\frac{5}{3}$

Also, the specific heat at constant volume is given by, $C_V=\frac{R}{\gamma -1}=\frac{3R}{2}$

In adiabatic process:

$\Rightarrow dQ=dU+dW=0$

$\Rightarrow dU=-dW=-6R$

$\Rightarrow C_{V}dT=-6R$

$\Rightarrow dT=-4$

This gives the final temperature as $(T-4)$ Kelvin.