A mixture contains 1 mode of helium $C_{p}$ = 2.5 R, $C_{v}$ = 1.5 R) and 1 a mole of hydrigen $(C_{p}$ = 3.5 R, $C_{v}$ = 2.5 R) Calculate the values of $C_{p}$ $C_{v}$ Calculate the values of $C_{p} C_{v}$ and $γ$ for the mixture.

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Solution

$C p^{'} = 2.5 R C p^{'} = 3.5 R$

$C v^{'} = 1.5 R C v^{'} = 2.5 R$

$n_{1} = n_{2} = 1 m o l,$

$[n_{1} + n_{2}] C v a T = n_{1} C v a T + n_{2} C^{'} v a T$

$\Rightarrow C v = \frac{n_{1} C v + n_{2} C^{'} v}{n_{2} + n_{2}}$

= $\frac{1.5 R + 2.5 R}{2} = 2 R$

Cp = Cv +R = 2R + R = 3R\)

$γ = \frac{C p}{C v} = \frac{3 R}{2 R}$ = 1.5

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(C_{P} = 2.5 R, C_{V} = 1.5 R)

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\frac{C_{p}}{C_{v}} = 5 / 3

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