`C_(p) and C_(v)` are specific heats at constant pressure and constant volume respectively. It is observed that
`C_(p) - C_(v) = a` for hydrogen gas
`C_(p) - C_(v) = b` for nitrogen gas
The correct relation between a and b is

Options

A. `a = 1/14 b`
B. `a = b`
C. `a = 14 b`
D. `a = 28 b`

Answer

C

Explanation

Molar specific heat of the gas at constant pressure,
`X_(p) = MC_(p)`
Molar specific heat of the gas at constant volume,
`X_(v) = MC_(v) :. X_(p) - X_(v) = R`
`:. C_(p) - C_(v) = R/M`
Then for hydrogen gas, `a = R/2 [ :. M_(H) = 2]`
and for nitrogen, `b = R/28 [ :. M_(N) = 28]`
`:. a/b = 28/2 or, a = 14 b`.