Find out the molar specific heats `C_(p) an C_(v)` of an ideal gas having `gamma = 1.67`. Given, `R = 2 cal cdot mol^(-1) cdot^(@)C^(-1)`.

Explanation

`gamma = (C_p)/(C_v) or C_(p) = gamma C_(v)`
For an ideal gas,
`C_(p) - C_(v) = R or gamma C_(v)^(.) - C_(v) = R or, C_(v)(gamma - 1) = R`
or, `C_(v) = R/(gamma - 1) = (2)/(1.67 -1) = 2/0.67 = 2.985 cal cdot mol^(-1) cdot^(@)C^(-1)`
`:. C_(p) = C_(v) + R = 2.985 + 2 = 4.985 cal cdot mol^(-1) cdot^(@)C^(-1)`.