Thermodynamics - Result Question 29
30. 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
[1998]
(a) $\frac{R}{(\gamma-1)}$
(b) $PV$
(c) $\frac{P V}{(\gamma-1)}$
(d) $\frac{\gamma P V}{(\gamma-1)}$
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Answer:
Correct Answer: 30. (c)
Solution:
- (c) Change in internal energy is equal to work done in adiabatic system
$\Delta W=-\Delta U$ (Expansion in the system)
$=-\frac{1}{\gamma-1}(P_1 V_1-P_2 V_2)$
$\Delta U=\frac{1}{1-\gamma}(P_2 V_2-P_1 V_1)$
Here, $V_1=V, V_2=2 V$
$\therefore \quad \Delta U=\frac{1}{1-\gamma}[P \times 2 V-P V]=\frac{P V}{1-\gamma}$
$\Rightarrow \Delta U=-\frac{P V}{\gamma-1}$
