During an adiabatic process , the pressure of a gas is proportional to the cube of its temperature . The value of `C_(I)//C_(v)` for that gas is

Options

A. `1/5`
B. `4/3`
C. `5/3`
D. `3/2`

Answer

D

Explanation

`P alpha T^(3)` …….(1)
In an adiabatic process,
`P alpha T^(gamma//gamma-1)` ………(2)
On comparing equations (1) and (2), we get,
`(gamma)/(gamma - 1) =3`
`implies gamma = (3)/(2)`
`therefore C_(p)/C_(v) = gamma=(3)/(2)`