First slide

Specific heat

Question

Four moles of hydrogen, 2 moles of helium and 1 mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?

Easy

A

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

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

R
D

$\frac{23}{7} R$

Solution

$C_{v}$ for hydrogen = 5R/2, Cv for helium = 3R/2, Cv for water vapour = 6R/2
${(C_{v})}_{m i x} = \frac{4 \times \frac{5 R}{2} + 2 \frac{3 R}{2} + 1 \times 3 R}{4 + 2 + 1} = \frac{16 R}{7}$
$C_{p} + C_{v} + R = \frac{16 R}{7} + R = \frac{23 R}{7}$

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