Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :
Solution
<p>Molar mass $M - {{2 \times 4 + n \times 1} \over {2 + n}}$ ..... (i)</p>
<p>Also, $$\gamma = {{{n_1}{C_{{P_1}}} + {n_2}{C_{{P_2}}}} \over {{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}}} = {{2 \times 5R + n \times 7R} \over {2 \times 3R + n \times 5R}}$$</p>
<p>$\Rightarrow \gamma = {{10 + 7n} \over {6 + 5n}}$ ...... (ii)</p>
<p>Given that ${V_{rms}} = \sqrt 2 \,{V_{sound}}$</p>
<p>$\Rightarrow \sqrt {{{3RT} \over M}} = \sqrt 2 \sqrt {{{\gamma RT} \over M}}$</p>
<p>$\Rightarrow \gamma = {3 \over 2}$</p>
<p>$\Rightarrow n = 2$</p>
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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