GATE 2023 AE – Question 33
The ratio of the speed of sound in H2 (molecular weight 2 kg/kmol) to that in N2 (molecular weight 28 kg/kmol) at temperature 300 K and pressure 2 bar is ____. (round off to two decimal places)
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Correct answer: 3.72 to 3.76
Explanation
The speed of sound in an ideal gas is
$$a=\sqrt{\gamma R T}=\sqrt{\frac{\gamma R_uT}{M}},$$
where $R_u$ is the universal gas constant and $M$ the molar mass.
H₂ and N₂ are both diatomic, so they have the same $\gamma=1.4$. Both are at 300 K, and the pressure does not affect the speed of sound of an ideal gas. So
$$\frac{a_{H_2}}{a_{N_2}}=\sqrt{\frac{M_{N_2}}{M_{H_2}}}=\sqrt{\frac{28}{2}}=\sqrt{14}=\mathbf{3.74}.$$