Question

In a certain gas, the ratio of the speed of sound and root mean square speed is \(\sqrt{\frac{5}{9}}\) gas undergoes a process given by PT = constant. The molar specific heat for the process is

(1) R/2

(2) 3R/2

(3) 5R/2

(4) 7R/2

Answer 1

(4) 7R/2

Given

speed of sound in gas / root mean squarespeed of gas = \(\sqrt{\frac{5}{9}}\)

The given gas is monoatomic. For the process gas undergoes PT = constant. Using ideal gas equation we rewrite the given relation as PV^1/2 = constant .

Comparing with PV^x = constant we have x = 1/2

Molar specific heat for the relation PV^x = constant is