Question 324: Thermodynamics & KTG

Question

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 :

Accepted Answer

Molar mass $$M - {{2 	imes 4 + n 	imes 1} \over {2 + n}}$$ ..... (i)
Also, $$\gamma  = {{{n_1}{C_{{P_1}}} + {n_2}{C_{{P_2}}}} \over {{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}}} = {{2 	imes 5R + n 	imes 7R} \over {2 	imes 3R + n 	imes 5R}}$$
$$ \Rightarrow \gamma  = {{10 + 7n} \over {6 + 5n}}$$ ...... (ii)
Given that $${V_{rms}} = \sqrt 2 \,{V_{sound}}$$
$$ \Rightarrow \sqrt {{{3RT} \over M}}  = \sqrt 2 \sqrt {{{\gamma RT} \over M}} $$
$$ \Rightarrow \gamma  = {3 \over 2}$$
$$ \Rightarrow n = 2$$

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Thermodynamics & KTG

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 :

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