At what temperature will the speed of sound in hydrogen be the same as in oxygen at 100°C ? Molar masses of…
At what temperature will the speed of sound in hydrogen be the same as in oxygen at 100°C ? Molar masses of oxygen and hydrogen are in the ratio 16 : 1 .
Solution
Sol. As we know, $v=\sqrt{\frac{\gamma RT}{M}}\;\Rightarrow\;v_{H_2}=v_{O_2}$
$\therefore\;\sqrt{\frac{\gamma_{H_2}R T_{H_2}}{M_{H_2}}}=\sqrt{\frac{\gamma_{O_2}R T_{O_2}}{M_{O_2}}}$
$\gamma_{H_2}=\gamma_{O_2}\qquad$(As both are diatomic)
$\therefore\;T_{H_2}=\left(\frac{M_{H_2}}{M_{O_2}}\right)(T_{O_2})=\left(\frac{1}{16}\right)(100+273)$
$=23.31\;\mathrm{K}\approx-249.7^\circ\mathrm{C}$
Answer: $23.31\;\mathrm{K}\approx-249.7^\circ\mathrm{C}$