`C_(p)` and `C_(v)` denote the molar specific heat capacities of a gas at constant pressure and volume respectively. Then `:`

Options

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

Answer

A

Explanation

If `C_(p)` and `C_(v)` are molar specific heats of a gas of molecular weight M. Then
`C_(p) - C_(v)=(R)/(M)`
For hydrogen, `C_(p) - C_(v) =a =(R)/(2)` ….(i)
For nitrogen, `C_(p) - C_(v) =b =(R)/(28)` ….(ii)
Dividing (i) by (ii), we get
`(a)/(b) =(R//2)/(R//28) =14` or `a=14 b`