During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio `C_P//C_V` for the gas is

Options

A. `4/3`
B. `2`
C. `5/3`
D. `3/2`

Answer

D

Explanation

(d) `p prop T^3 rArr PT^-3=constant…(i)`
But for an adiabatic process, the pressure temperature
relationship is given by
`P^(gamma-1)T^(gamma)=constant rArr PT^(gamma/(1-gamma))=constt….(ii)`
From (i) and (ii) `gamma/(1-gamma)=-3 rArr gamma=-3+3gamma rArr gamma=3/2`