First slide

Law of equipartition of energy

Question

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?

Moderate

A

$\frac{16}{7} R$
B

$\frac{7 R}{16}$
C

R
D

$\frac{23}{7} R$

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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