A gaseous mixture enclosed in a vessel consists of one mole of a gas A with $γ = (\frac{5}{3})$ and some amount of gas B with $γ = (\frac{7}{5})$ at a temperature T. The gases A and B do not react with each other and are assumed to be ideal. Find the number of moles of the gas B if $γ$ for the gaseous mixture is $(\frac{19}{13})$ .

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Detailed Solution

AS FOR IDEAL GAS $C_{p} - C_{u} = R$ and $γ = (\frac{C_{P}}{C_{υ}})$
SO $C_{υ} = \frac{R}{(γ - 1)}$
$\begin{array}{l} ∴ {(C_{ν})}_{1} = \frac{R}{(\frac{5}{3}) - 1} = \frac{3}{2} R \\ {(C_{ν})}_{2} = \frac{R}{(\frac{7}{5}) - 1} = \frac{5}{2} R \end{array}$
Now from conservation of energy,
$\begin{array}{l} i . e, Δ U = Δ U_{1} + Δ U_{1} \\ (μ_{1} + μ_{2}) {(C_{ν})}_{m i x} Δ T = [μ_{1} {(C_{υ})}_{1} + μ_{2} {(C_{υ})}_{2}] Δ T \end{array}$