Question

For monoatomic gas which is correct?

• A. $ C_{V}=\frac{3}{5}R $
• B. $ C_{P}=\frac{5}{2}R $
• C. $ C_{P}-C_{V}=2R $
• D. $ \frac{C_{P}}{C_{V}}=\frac{3}{5} $

Answer 1

Answer: (B)

Monoatomic gas has three translational degrees of freedom. Specific heat at constant volume
$ (C_{V})=\frac{f}{2}R $ and specific heat at constant pressure $ (C_{P}) $
$ C_{P}=\left( \frac{f}{2}+1 \right)R\, $
For monoatomic gas
$ f=3 $
$ \therefore C_{V}=\frac{3}{2}R,C_{P}=\left( \frac{3}{2}+1 \right)R=\frac{5}{2}R $
From Mayors formula
$ C_{P}-C_{V} =R $
$ \therefore \frac{5}{2}R-\frac{3}{2}R=R $
and $ \gamma =\frac{C_{P}}{C_{V}}=\frac{5/2}{3/2}=\frac{5}{3} $