First slide

Law of equipartition of energy

Question

I mole of gas having $γ = \frac{7}{5}$ is mixed with I mole of a gas having $γ = \frac{4}{3}$ . What will be the $γ$ for the mixture?

Moderate

A

$\frac{5}{11}$
B

$\frac{15}{13}$
C

$\frac{15}{11}$
D

$\frac{5}{13}$

Solution

For $γ = \frac{7}{5} C_{v} = \frac{R}{γ - 1} = \frac{R}{\frac{7}{5} - 1} = \frac{5 R}{2}$
$C_{p} = \frac{γR}{γ - 1} = \frac{(\frac{7}{5}) R}{\frac{7}{5} - 1} = \frac{7 R}{2}$
For $γ = \frac{4}{3} C_{v} = 3 R, C_{p} = 4 R$
$∴ γ_{mix} = \frac{\frac{7}{2} + 4}{\frac{5}{2} + 3} = \frac{15}{11}$

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