First slide

Law of equipartition of energy

Question

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{P} a n d C_{υ}$ respectively. If $γ = \frac{C_{p}}{C_{υ}}$ and R is the universal gas constant, then $C_{υ}$ is equal to

Moderate

A

$\frac{(γ - 1)}{R}$
B

$γ R$
C

$\frac{1 + γ}{1 - γ}$
D

$\frac{R}{(γ - 1)}$

Solution

For an ideal gas
$C_{p} - C_{v} = R - - - (i) \frac{C_{p}}{C_{v}} - 1 = \frac{R}{C_{v}} A s γ = \frac{C_{p}}{C_{v}} ∴ γ - 1 = \frac{R}{C_{v}} C_{v} = \frac{R}{γ - 1}$

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