A gas undergoes a process in which its pressure `P` and volume `V` are related as `VP^(n) =` constant. The bulk modulus of the gas in the process is:

Options

A. `np`
B. `p^((1)/(n))`
C. `(p)/(n)`
D. `p^n`

Answer

C

Explanation

`Vp^n=`constant
`Vnp^(n-1)dP+p^ndV=0`
`(dp)/(dV)=-(p)/(nV)`
Bulk modulus`=-(dp)/((dV)/(V))=-V(dp)/(dV)`
`=(-V)(-(P)/(nV))`
`=(P)/(n)`