First slide

Law of equipartition of energy

Question

When I mole of a monatomic gas is mixed with 3 moles of a diatomic gas, the value of adiabatic exponent $γ$ for the mixture is:

Moderate

A

$\frac{5}{3}$
B

1.5
C

1.4
D

$\frac{13}{9}$

Solution

$\frac{n_{1} + n_{2}}{γ - 1} = \frac{n_{1}}{γ_{1} - 1} + \frac{n_{2}}{γ_{2} - 1}$
$\frac{1 + 3}{γ - 1} = \frac{1}{\frac{5}{3} - 1} + \frac{3}{\frac{7}{5} - 1}$
$\frac{4}{γ - 1} = \frac{3}{2} + \frac{15}{2} = 9$
or $γ - 1 = \frac{4}{9} \Rightarrow γ = 1 + \frac{4}{9} = \frac{13}{9}$

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