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

Answer

B

Explanation

Given : `PpropT^(3)" "...(1)`
For an adiabatic change, `P^(1-gamma)T^(gamma)` = constant
`thereforeP^(1-gamma)prop1/T^(gamma)" "thereforePpropT^(gamma/(gamma-1))" "...(2)`
From (1) and (2), we find that `gamma/(gamma-1)=3`
`thereforegamma=3gamma-3" "therefore2gamma=3" "thereforegamma=3/2`