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 = C_p/C_V`
B. `n=(C - C_p)/(C-C_V)`
C. `n = (C_p -C)/(C - C_V)`
D. `n = (C - C_V)/(C-V_p)`

Answer

B

Explanation

For polytropic process, specific heat for an ideal gas.
`C=(R )/(1-n)+C_(v)" ":. (R )/(1-n)+C_(v)=C`
`(R )/(1-n)=C-C_(v) implies (R )/(C-C_(v))=1-n` (where, `R=C_(p)-C_(v))`
`implies (C_p - C_v)/(C-C_v)=1-n implies n=1-(C_p-C_v)/(C-C_v) implies n=(C-C_p)/(C-C_v)`
Thus, number of moles n is given by `n=(C-C_p)/(C-C_v)`.