Thermodynamics Ques 25
25. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$, the change in internal energy of a mass of gas, when the volume changes from $V$ to $2 V$ at constant pressure $P$, is $\frac{3}{2}nR\Delta T$
[1998]
(a) $\frac{R}{(\gamma-1)}$
(b) $PV$
(c) $\frac{P V}{(\gamma-1)}$
(d) $\frac{\gamma P V}{(\gamma-1)}$
Show Answer
Answer:
Correct Answer: 25.(c)
Solution:
- (c) Change in internal energy is equal to the negative of work done in an adiabatic system
$\Delta W=-\Delta U$ (Expansion in the system)
$=-\frac{1}{\gamma-1}(P_1 V_1-P_2 V_2)$
$\Delta U=\frac{1}{\gamma-1}(P_2 V_2-P_1 V_1)$
Here, $V_1=V, V_2=2 V$
$\therefore \quad \Delta U=\frac{1}{\gamma-1}[P \times 2 V-P V]=\frac{P V}{\gamma-1}$
$\Rightarrow \Delta U=\frac{P V}{\gamma-1}$
BETA
