Question

Calculate the ratio of the speed of sound in neon to that in water vapours at any temperature. (molecular weight of neon $=2.02\times {10}^{-2}kg{mole}^{-1}$ and for water vapours $=1.8\times {10}^{-2}kg{mole}^{-1}$)

Answer 1

Velocity of sound in gas $v=\sqrt{\frac{\gamma RT}{M}}$
Thus we get $v=\sqrt{\frac{1}{M}}$
$⟹$ $\frac{v_n}{v_w}=\sqrt{\frac{M_w}{M_n}}$
Given : $M_n=2.02\times {10}^{-2}kg/mole$ and $M_w=1.8\times {10}^{-2}kg/mole$
$\therefore$ $\frac{v_n}{v_w}=\sqrt{\frac{1.8\times {10}^{-2}}{2.02\times {10}^{-2}}}=0.94$