One mole of a monatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is___________.

Explanation

The volume of `gamma` of the mixture is given by
`(n_(1) + n_(2))/(gamma -1) = (n_(1))/(gamma_(1) - 1) + (n_(2))/(gamma_(2) - 1)`
`:. (1 + 1)/(gamma - 1) = (1)/((5)/(3) - 1) + (1)/((7)/(5) - 1)` or `gamma = 1.5`
In general, `C_(v) = (R )/(gamma - 1)`
`= (R )/(1.5 - 1) = 2 R`
Hence, the specific heat of the mixture is `2R`.