An ideal gas under goes a quasi static, reversible process in whichh 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 pressur and constant volume, respectively):

Options

A. `n=(C_P-C)/(C-C_V)`
B. `n=(C-C_V)/(C-C_P)`
C. `n=(C_P)/(C_V)`
D. `n=(C-C_P)/(C-C_V)`

Answer

D

Explanation

(d) For a polytropic process
`C=C_v+R/(1-n) :. C-C_v=R/(1-n)`
`:. 1-n=R/(C-C_v) :. 1-R/(C-C_v)=n`
`:.n=(C-C_v-R)/(C-C_v)=(C-C_v-C_p+C_v)/(C-C_v)`
`=(C-C_p)/(C-C_v) (:' C_p-C_(v=R))`