If for hydrogen `C_(P) - C_(V) = m` and for nitrogen `C_(P) - C_(V) = n`, where `C_(P)` and `C_(V)` refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between `m` and `n` is (molecular weight of hydrogen = 2 and molecular weight or nitrogen = 14)

Options

A. `n = 14m`
B. `n = 7m`
C. `m = 7n`
D. `m = 14n`

Answer

C

Explanation

`:. M=7n` and `C_(p)-C_(v)=m` for hydrogen `(M_(1)=2)`
`C_(p) - C_(v) = n` for nitrogen `(M_(2)=14)`
For hydrogen `C_(P) - C_(V) = 1/(M_1) (dQ)/(dT) = m`
For nitrogen ,`C_(P) - C_(V) = 1/(M_2) (dQ)/(dT) = n`
`:. (m)/(n) = (1/(M_1) (dQ)/(dT))/(1/(M_2) (dQ)/(dT)) = (M_2)/(M_1)=14/2 = 7`.