Question

Relation between the ratio of specific heats $(\gamma)$ of gas and degree of freedom ' $f$ ' will be

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

Answer 1

Answer: (C)

$\gamma=\frac{ C _{ P }}{ C _{ V }}=\frac{ C _{ V }+ R }{ C _{ V }} $
$=\frac{\frac{1}{2} fR + R }{\frac{1}{2} fR }=\frac{ f +2}{ f }$
$\Rightarrow \gamma f - f =2$
$ \Rightarrow f =\frac{2}{\gamma-1}$