Question

If c_p and c_v denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

1) c_p-c_v = R/28

2) c_p-c_v =R/14

3) c_p-c_v = R

4) c_p-c_v = 28R

Answer 1

Step 1:

As we know, molar heat capacity is given by the product of the molar mass and specific heat capacity.

So, at constant pressure and constant volume the molar heat capacities will be $28C_{p}and28C_v$ respectively (molar mass of nitrogen = 28u).

Step 2:

As nitrogen is a diatomic gas.
In case of diatomic gases:-
Specific heat of one gram mole of gas at constant volume ($C_v$ ) is, $\frac{5}{2}R$
and Specific heat of one gram mole of gas at constant pressure (C_p) is, $\frac{7}{2}R$

Subtracting eq 1 from eq 2, we get :-
$C_p-C_v=R$ where R is a gas constant.

Step 3:

$\therefore 28C_p-28C_v=R$

and $C_p-C_v=\frac{R}{28}$

Hence, option (A) is correct.