In a certain gas, the ratio of the velocity of sound and root mean square velocity is `sqrt(5//9)`. The molar heat capacity of the gas in a process given by `PT = constant` is.
(Take `R = 2 cal//mol K`). Treat the gas as ideal.

Options

A. `R//2`
B. `3R/2`
C. `5R/2`
D. `7R/2`

Answer

D

Explanation

`(V_(sound))/(V_(rms)) =(sqrt((gammaP)/(rho)))/(sqrt((P3)/(rho))) = sqrt(5/9)x`
`PT =` constnat
`P^(2)V = const implies PV^(1//2)=` constant ltbr gt`implies x = 1/2`
`C = C_(v)+(R)/(1-x) = 3/2 R +2R = (7R)/(2)`.