First slide

Law of equipartition of energy

Question

The ratio of the specific heats $\frac{C_{p}}{C_{v}} = γ$ in terms of degrees of freedom (n) is given by

Easy

A

$(1 + \frac{2}{n})$
B

$(1 + \frac{n}{2})$
C

$(1 + \frac{1}{n})$
D

$(1 + \frac{n}{3})$

Solution

$For n degrees of freedom, C_{v} = \frac{n}{2} R$
$Also, C_{p} - C_{v} = R$
$C_{p} = C_{v} + R = \frac{n}{2} R + R$
$C_{p} = (\frac{n}{2} + 1) R$
$γ = \frac{C_{p}}{C_{v}} = \frac{(\frac{n}{2} + 1) R}{(n / 2) R} = \frac{n + 2}{n} ∴ γ = 1 + \frac{2}{n}$

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