Question

If the degree of freedom of a gas molecule is $f$ , then the ratio of two specific heats is given by

• A. $\frac{2}{f}+1$
• B. $1-\frac{2}{f}$
• C. $1+\frac{1}{f}$
• D. $1-\frac{1}{f}$

Answer 1

Answer: (A)

The molar specific heat capacity at constant volume is given by
$C_{v}=\frac{f}{2}R$
According to Mayer's relation, the molar specific heat capacity at constant pressure
$C_{p}=C_{v}+R\Rightarrow C_{p}=\frac{f}{2}R+R=\left(\frac{f}{2} + 1\right)R$
The ratio of specific heats
$\gamma =\frac{C_{p}}{C_{v}}=\frac{\left(\frac{f}{2} + 1\right) R}{\frac{f}{2} R}=1+\frac{2}{f}$