An ideal gas under goes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by `PV^n=constant`, then n is given by (Here `C_P and C_V` are molar specific heat at constant pressure and constant volume, respectively):

Options

A. `n=gamma-1`
B. `n=gamma`
C. `n=gamma+1`
D. `n=1-gamma`

Answer

B

Explanation

`s=(dQ)/(mxxdT)` but s = 0 means dQ = 0
i.e. no heat is given or taken out from the system
i.e. the change is adiabatic
and for an adiabatic change `PV^(gamma)` = constant
But it is given that `PV^(n)` = constant
`thereforen=gamma`