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

Answer

A

Explanation

The equation of adiabatic change is
`P_V^(gamma)` = constant which gives
`P^(1-gamma)T^(gamma)` = constant
`P^(1-gamma)alpha1/T^gamma" or " P alphaT(gamma/(gamma-1))`
As`p alpha T^3:. gamma/(gamma-1)=3 " or " gamma=3/2`
Hence `C_P/C_V = =gamma=3/2`