# A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $\dpi{100} C_{P}/C_{V}$ of the mixture is Option 1) $1.4\; \;$ Option 2) $\; 1.54\;$ Option 3) $\; 1.59\;$ Option 4) $\; 1.62$

V Vakul

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

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

$n_{1} = \frac{16}{4} = 4, C_{v1} = \frac{3R}{2}, C_{p1} = \frac{5R}{2}$

$n_{2} = \frac{16}{32} = \frac{1}{2}, C_{v2} = \frac{5R}{2}, C_{p2} = \frac{7R}{2}$

$\gamma ^{mix} = \frac{10R+\frac{7R}{4}}{6R+\frac{5R}{4}}$

$= \frac{47}{29} = 1.62$



Option 1)

$1.4\; \;$

This option is incorrect.

Option 2)

$\; 1.54\;$

This option is incorrect.

Option 3)

$\; 1.59\;$

This option is incorrect.

Option 4)

$\; 1.62$

This option is correct.

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