Question

The constant $\gamma$ for oxygen as well as for hydrogen is $1.40$. If the speed of the sound in oxygen is $470{\text{ms}}^{-1}$, what will be the speed in hydrogen at the same temperature and pressure ?

• A. $470{\text{ms}}^{-1}$
• B. $940{\text{ms}}^{-1}$
• C. $1880{\text{ms}}^{-1}$
• D. $235{\text{ms}}^{-1}$

Answer 1

The correct option is C $1880{\text{ms}}^{-1}$

Speed of sound in a gas is given by

$V=\sqrt{\frac{\gamma P}{\rho }}$

At $STP$, $22.4$ litres of oxygen has a mass of $32\text{g}$. Whereas, the same volume of hydrogen has a mass of $2\text{g}$.

Thus, the density of oxygen is $16$ times the density of hydrogen at the same temperature and pressure.

So, $\frac{{\rho }_{O_2}}{{\rho }_{H_2}}=16$

Since, $\gamma$ is same for both the gases,

$\frac{V_{H_2}}{V_{O_2}}=\sqrt{\frac{{\rho }_{O_2}}{{\rho }_{H_2}}}=\sqrt{16}=4$

$\Rightarrow V_{H_2}=4\times V_{O_2}=4\times 470$

$\therefore V_{H_2}=1880{\text{ms}}^{-1}$

Hence, option $\left(C\right)$ is correct.

Why this question ? Concept : At the same temperature and pressure, density of gas is directly proportional to molar mass of the gas.