The molar specific heats of an ideal gas at constant pressure and volume are denotes by `C_(P)` and `C_(upsilon)` respectively. If `gamma = (C_(P))/(C_(upsilon))` and `R` is the universal gas constant, then `C_(upsilon)` is equal to

Options

A. `(Rgamma)/(gamma-1)`
B. `gammaR`
C. `(1+gamma)/(1-gamma)`
D. `R/(gamma-1)`

Answer

A

Explanation

Given, that `(C_(p))/(C_(v))=gamma`
As we ~now that from Mayer's relation, `C_(p)-C_(v)=R`
where, R = universal gas constant
Substitute the value of `C_(p)` from the above relation in Eq. (i), we get
`gamma=(C_(p))/(C_(p)-R)`
`gamma(C_(p)-R)=C_(p)`
`rArrgammaC_(p)-C_(p)=gammaR`
`C_(p)(gamma-1)=gammaR`
`gammaC_(p)=(gammaR)/(gamma-1)`
Hence, `C_(p)` is equal to `(gammaR)/(gamma-1)`