The value of molar specific heat at constant volume for 1 mol of polyatomic gas having n number…

Q: The value of molar specific heat at constant volume for 1 mol of polyatomic gas having n number of degrees of freedom at temperature TK is: (R = universal gas constant)

(a) (n R)/(2 T)

(b) (n R)/2

(c) (n RT)/2

(d) 2 n RT

Ans: (b)

Sol: According to law of equipartition of energy average KE per molecule per degree of freedom at temperature T is (1/2) kT.
The average KE per molecule of polyatomic gas molecule = (n/2) kT .

The average KE per mole of polyatomic gas is

$ \displaystyle E = \frac{n}{2}k T \times N = \frac{n}{2}R T$

$ \displaystyle C_v = \frac{d}{dT}(\frac{n}{2}R T) $

$ \displaystyle C_v = \frac{n}{2}R $