# If $\dpi{100} C_{P}$ and $\dpi{100} C_{V}$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then Option 1) $C_{P}-C_{V}=28/R$ Option 2) $C_{P}-C_{V}=R/28$ Option 3) $C_{P}-C_{V}=R/14$ Option 4) $C_{P}-C_{V}=R$

As we learnt in

Specific heat in isobaric process -

$C_{p}= \left ( \frac{f}{2}+1 \right )R$

$\gamma^{mix}=\frac{n_{1}C_{p1}+n_{2}C_{p2}}{n_{1}C_{v1}+n_{2}C_{v2}}$

- wherein

$f$ is degree of freedom

Difference between moler specific heat = R

$C_{p}\:-C_{v}\:=R$

1 mole = 28g of nitrogen.

$\therefore \:C_{p}\:-C_{v}\:=\frac{R}{28}$

where $C_{p}$ & $C_{v}$ denote specific heats of nitrogen per unit mass.

Option 1)

$C_{P}-C_{V}=28/R$

This option is incorrect.

Option 2)

$C_{P}-C_{V}=R/28$

This option is correct.

Option 3)

$C_{P}-C_{V}=R/14$

This option is incorrect.

Option 4)

$C_{P}-C_{V}=R$

This option is incorrect.

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