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

a. Given `P prop T^(3)`. But for adiabatic process `P prop T^(gamma//gamma -1)`. So,
`(gamma)/(gamma -1) = 3 implies gamma = (3)/(2) implies (C_(P))/(C_(v)) = (3)/(2)`