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 `PV^(gamma) = "constant"`, which gives
`P^(1-gamma)T^(gamma)=constant`
`:. P^(1-gamma) prop1/(T^(gamma)) or P prop T^(gamma//(gamma-1))`
As `P propT^(3) :. (gamma)/(gamma-1)= 3 or gamma= 3/2`
Hence `(C_(p))/(C_(v))= gamma= 3/2`