For adiabatic expansiion of a perfect gas, `(dP)/(P)` is

Options

A. `(dV)/(V)`
B. `gamma.(dV)/(V)`
C. `-gamma(dV)/(V)`
D. `-gamma^(2)(dV)/(V)`

Answer

C

Explanation

For adiabatic expansion, `PV^(gamma) =` constnat
On differentiating, `P.gamma.V^(gamma-1)dV +V^(gamma) dP = 0 -Pgamma V^(gamma-1) dV = V^(gamma)dP`
or `(dP)/(P) =- gamma.(V^(gamma-1))/(V^(gamma))dV =- gamma.(dV)/(V)`.