First slide

Change in internal energy

Question

The ratio of specific heats of a gas is x. The change in internal energy of one mole of the gas, when the volume changes from V to 3V at constant pressure P is

Moderate

A

$\frac{P V}{x}$
B

$P V$
C

$\frac{2 P V}{(x - 1)}$
D

$\frac{x P V}{(x - 1)}$

Solution

$W = P (3 V - V) = 2 P V$
initial temperature is T, final temperature $T^{1} = 3 T$
$∴ Δ U = 1. C_{V} . Δ T = \frac{R}{(x - 1)} . (3 T - T) = \frac{2 R T}{x - 1} = \frac{2 P V}{(x - 1)} [∵ P V = 1. R T]$

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