Question
If $${C_P}$$ and $${C_V}$$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
A.
$${C_P} - {C_V} = 28\,R$$
B.
$${C_P} - {C_V} = \frac{R}{{28}}$$
C.
$${C_P} - {C_V} = \frac{R}{{14}}$$
D.
$${C_P} - {C_V} = R$$
Answer :
$${C_P} - {C_V} = \frac{R}{{28}}$$
Solution :
According to Mayer's relationship $${C_P} - {C_V} = R$$
$$\therefore \,\,\frac{{{C_P}}}{M} - \frac{{{C_V}}}{M} = \frac{R}{M}\,\,\,\,{\text{Here }}M = 28.$$