During a reversible 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. `7/2`
C. `5/3`
D. `9/7`

Answer

A

Explanation

For adiabatic reversible process,
`TP^((1-gamma)/(gamma))=`constant
or, `PT^((gamma)/((1-gamma))=`constant . . . (1)
Again as mentioned, `P prop T^(3)`
or, `PT^(-3)`=constant . . . (2)
Comparing equation (1) and (2), it may be written as,
`(gamma)/(1-gamma)=-3`
or, `gamma=-3+3gamma or, 2gamma=3`
`therefore gamma=(3)/(2)`.