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Heat and Thermodynamics

Section: Physics

Question : 47 of 73

Marks: +1, -0

The average energy per mole of the gas mixture is 2RT
The ratio of speed of sound of i the gas mixture to that in helium gas is $\sqrt{\frac{6}{5}}$ .
The ratio of the rms speed of helium atoms to that hydrogen molecules is $\frac{1}{2}$
The ratio of the rms speed of helium atoms to that hydrogen molecules is $\frac{1}{\sqrt{2}}$

Solution:

U=nC_{v_1}T+nC_{v_2}T

=1\times\frac{5}{2}RT+\frac{3}{2}RT=4RT

\Rightarrow 2C_{V_{mix}}T=4RT

Average energy per mole

=2RT\Rightarrow C_{V_{mix}}=2R

\frac{C_{mix}}{C_{Ho}}=\sqrt{\left(\frac{\gamma_{mix}}{\gamma_{Ho}}\right)\left(\frac{M_{He}}{M_{mix}}\right)}=

\sqrt{\frac{3}{2}\times\frac{3}{5}\times\frac{4}{3}}=\sqrt{\frac{6}{5}}

\frac{V_{rms}\mathrm{He}}{V_{rms}\mathrm{H}_2}

=\sqrt{\frac{M_{\mathrm{H}_2}}{M_{\mathrm{He}}}}=\frac{1}{\sqrt{2}}

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