Question

if cp and cv denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then 1) cp-cv = r/28 2) cp-cv = r/14 3) cp-cv = r 4) cp-cv = 28r

Answer 1

As nitrogen is a diatomic gas.
In case of diatomic gases:-
Specific heat of one gram mole of gas at  constant volume (Cv) is given by :- Cv = 52R  ........(1)
and Specific heat of one gram mole of gas at  constant pressure  (Cp) is given by :- Cp=72R.....(2)
Subtracting eq 1 from eq 2, we get :-
 Cp - Cv = R  where R is a gas constant

Answer 2

In case of diatomic gases like nitrogen
specific heat of 1gm mole of gas at constant volume= Cv= 5/2 R
specific heat of 1gm mole of gas at constant pressure = Cp= 7/2 R

subtracting both equations we get
Cp - Cv = R