First slide

Law of equipartition of energy

Question

lf the ratio of specific heat of a gas at constant pressure to that at constant volume is $γ$ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is

Moderate

A

$\frac{R}{(γ - 1)}$
B

pV
C

$\frac{pV}{(γ - 1)}$
D

$\frac{γpV}{(γ - 1)}$

Solution

$∆ U = {nC}_{v} ∆ T$
Also, $\frac{C_{p}}{C_{v}} = γ . Hence \frac{C_{p} - C_{v}}{C_{v}} = γ - 1$
This is $C_{v} = \frac{R}{(γ - 1)} . This gives$
$∆ U = \frac{nR}{γ - 1} ∆ T = \frac{p ∆ V}{γ - 1} = \frac{p (2 V - V)}{γ - 1} = \frac{pV}{γ - 1}$

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