Question

At what temperature will the speed of sound in hydrogen be the same as in oxygen at 100${}^{\circ }$ C? Molar masses of oxygen and hydrogen are in the ratio 16:1.

• A. 273 k
• B. 300 k
• C. 23 k
• D. 50 k

Answer 1

The correct option is C

23 k

$v=\sqrt{\frac{\gamma RT}{M}}$

$v{{}_H}_2=v{{}_O}_2$

$\therefore \sqrt{\frac{\gamma H_{2}RT{H}_2}{M{H}_2}}=\sqrt{\frac{\gamma O_{2}RT{O}_2}{M{O}_2}}$

$\gamma {{}_H}_2=\gamma {{}_O}_2$ (as both are diatomic)

$\therefore T{{}_H}_2$$=\left(\frac{M{H}_2}{M{O}_2}\right)\left(T{{}_O}_2\right)$$=\left(\frac{1}{16}\right)(100+273)$

=23.31 K

$\approx -{249.7}^{\circ }C$.