During an adiabatic process, the pressure of gas is found to be proportional to the cube of its absolute temperature. The ratio of `(C_(p,m)//C_(v,m))` for gas is :

Options

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

Answer

A

Explanation

Given ` P alpha T^(3)`
`because PV = muRT`
`therefore P alpha (PV)^(3) implies P^(3)V^(3)alphaP implies P^(2)V^(3)` = constant
`implies PV^(s//2)` = constant `implies gamma = (C_(P))/(C_(V)) = (3)/(2)`