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

Given ` p propto T^3" ""………….."(i)`
In an adiabatic process,
`T^(gamma)p^(1-gamma)`= constant `[" as "gamma=(C_p)/(C_v)]`
`T propto (1)/(p^(1-gamma)"/"gamma)`
`T^(gamma"/"gamma-1) propto p`
Comparing Eqs. (i) and (ii), we get
`(gamma)/(gamma-1)=3 " or "3gamma-3=gamma` or `2gamma=3 " or "(C_p)/(C_v)=gamma=(3)/(2)`.