Question

At what temperature will the speed of sound in hydrogen be the same as in oxygen at ${100}^0$ C? Molar masses of oxygen and hydrogen are in the ratio 16:1.

• A. $-{249.7}^{0}C$
• B. $-{257}^{0}C$
• C. $-{57}^{0}C$
• D. $-{17}^{0}C$

Answer 1

The correct option is A

$-{249.7}^{0}C$

$v=\sqrt{\frac{\gamma RT}{M}}{v}_{H_2}=v_{O_2}\therefore \sqrt{\frac{{\gamma }_{H_2}R{T}_{H_2}}{M_{H_2}}}=\sqrt{\frac{{\gamma }_{O_2}R{T}_{O_2}}{M_{O_2}}}{\gamma }_{H_2}={\gamma }_{O_2}\text{(}asbotharediatomic)\therefore T_{H_2}=\left(\frac{M_{H_2}}{M_{O_2}}\right)(T_{O_2})=\left(\frac{1}{16}\right)(100+273)=23.31K\approx -{249.7}^{0}C$