A mixture contains 1 mole of helium ( $C_{p} = 2.5 R, C_{v} = 1.5 R$ ) and 1 mole of hydrogen ( $C_{p} = 3.6 R, C_{v} = 2.5 R$ ). Calculate the volue of $C_{p}, C_{v}$ and $γ$ for the mixture.

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Solution

If $G$ heat is given
to the mixture
And,
the $H e$ absorbs
$q_{1}$ and $H_{2}$ absorbs
$q_{2}$ amt of heat
then,
$G = V_{1} + V_{2} . . . . . . (i)$
If the rise in temperature is $Δ T$
then
$q_{1} = n_{1} (C_{p})_{H e} Δ T$
$q_{2} = n_{2} (C_{p})_{H e} Δ T$
$G = (n_{1} + n_{2}) (C_{p})_{m i x} Δ T$
putting the values on $(i)$
$(n_{1} + n_{2}) (C_{p})_{m i x} Δ T = n_{1} (C_{p})_{H e} Δ T + n_{2} (C_{p})_{H_{2}} Δ T$
$2 C_{p_{m i x}} Δ T = 2.5 R Δ T + 3.6 R Δ T$
$2 C_{p_{m i x}} = 6.1 R$
$C_{p_{m i x}} = \frac{6.1}{2} R$
$C_{p_{m i x} = 3.05 R}$

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A mixture contains 1 mole of helium (Cp=2.5R,Cv=1.5R) and 1 mole of hydrogen (Cp=3.6R,Cv=2.5R). Calculate the volue of Cp,Cv and γ for the mixture.

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