Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?

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$\frac{16}{7} R$

$\frac{23}{7} R$

$\frac{7 R}{16}$

answer is D.

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Detailed Solution

$C_{v}$ for hydrogen = $\frac{5 R}{2}, C_{v} for helium = \frac{3 R}{2}$

$C_{v} for water vapour = \frac{6 R}{2}$

$∴ {[C_{v}]}_{mix} = \frac{4 \times \frac{5 R}{2} + 2 \frac{3 R}{2} + 1 \times 3 R}{4 + 2 + 1} = \frac{16 R}{7}$

$∴ C_{p} + C_{v} + R = \frac{16 R}{7} + R = \frac{23 R}{7}$

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