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:

  1. (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, $V_1=V, V_2=2 V$

$\therefore \quad \Delta U=\frac{1}{1-\gamma}[P \times 2 V-P V]=\frac{P V}{1-\gamma}$

$\Rightarrow \Delta U=-\frac{P V}{\gamma-1}$