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 adiabatic process `P prop T^(3)`
Ideal gas equation `implies T = (PV)/(nR)`
`PV = nRT`
`P prop T^(3)`
`P prop (PV)^(3)`
`implies P^(2)V^(3)` = constant
`or PV^(3/2) = consta nt`
Hence, `gamma= 3/2`.