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

Answer

A

Explanation

Since , `C=C_v+(R)/(1-n)`
`implies C-C_v=(C_p-C_v)/(1-n) implies 1-n=(C_p-C_v)/(C-C_v)`
`n=1-((C_p-C_v)/(C-C_v))=((C-C_p)/(C-C_v))`