For an adiabatic expansion of a perfect gas `dP//P` is equal to :

Options

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

Answer

C

Explanation

`PV^(gamma)=`constant
`PgammaV^(gamma-1)dV+V^(gamma)dP=0`
`-gammaV^(gamma-1).dV=V^(gamma)(dP)/P`
`:. (dP)/P=(-gammaV^(gamma-1))/(V^(gamma))xxdV=(-gammadV)/(V)`