The temperature of an ideal gas undergoing adiabatic expansion varies with volume as `T prop V^(-(3)/(4))`, then the value of `(C_(P))/(C_(V))` for the gas is

Options

A. `(3)/(5)`
B. `(5)/(3)`
C. `(7)/(3)`
D. `(7)/(4)`

Answer

D

Explanation

Given
`T prop V^(-3//4)`
`implies TV^(3//4) `= Constant
Comparing it with the relation for the adiabatic process we get
`TV^(gamma-1) = TV^(3//4) `
`implies gamma -1 = (3)/(4)`
`implies gamma = (7)/(4)`