Question

The ratio of specific heats $\left(\frac{C_{P}}{C_{V}}\right)$ in terms of degree of freedom $(f) $ is given by:

• A. $\left(1+\frac{ f }{3}\right)$
• B. $\left(1+\frac{2}{ f }\right)$
• C. $\left(1+\frac{ f }{2}\right)$
• D. $\left(1+\frac{1}{f}\right)$

Answer 1

Answer: (B)

Molar heat capacity at constant volume $C _{ V }=\frac{f R }{2}$
where $f$ is degree of freedom.
Molar heat capacity at constant pressure can be written as
$C _{ P }= R + C _{ V }= R +\frac{ fR }{2}=\left(1+\frac{ f }{2}\right) R$
So $\frac{C_{P}}{C_{v}}=1+\frac{2}{f}$