Question

At what temperature the speed of sound in nitrogen will be equal to the speed of sound in oxygen at ${55}^{\circ }C$

• A. ${14}^{\circ }C$
• B. ${28}^{\circ }C$
• C. ${42}^{\circ }C$
• D. ${70}^{\circ }C$

Answer 1

The correct option is A ${14}^{\circ }C$

We know that,

$v=\sqrt{\frac{\gamma RT}{M}}$ where, $\gamma$ = Adiabatic constant, $R$ = Universal gas constant, $M$ = Molar mass.

$v\propto \sqrt{\frac{T}{M}},\gamma =1.4$ for both because they have same molecular nature.

So,

$\frac{T_N}{M_N}=\frac{T_O}{M_O}$

$\frac{T_N}{28}=\frac{273+55}{32}$

$T_N=287K\Rightarrow T_N={14}^{o}C$

So, A is the correct answer.