Question

At the same temperature and pressure, the ratio of the sound velocity in oxygen to that in hydrogen is about.

• A. $16:1$
• B. $1:16$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is C

$4:1$

Explanation for the correct option:

C. $4:1$

Velocity of sound in a gas, $\mathrm{v}=\surd \mathrm{\gamma RT}/\mathrm{M}$

where, $\begin{array}{rcl}\mathrm{\gamma }& =& \mathrm{ratio}\mathrm{of}\mathrm{specific}\mathrm{heats}\mathrm{at}\mathrm{constant}\mathrm{pressure}\mathrm{and}\mathrm{temperature},\\ \mathrm{T}& =& \mathrm{absolute}\mathrm{temperature}\mathrm{of}\mathrm{the}\mathrm{gas},\\ \mathrm{M}& =& \mathrm{molecular}\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{gas},\\ \mathrm{R}& =& \mathrm{gas}\mathrm{constant},\end{array}$

At $\mathrm{STP}$, temperature $\mathrm{T}$ of both the given gases will be the same, and as both the gases are diatomic so $\mathrm{\gamma }$ is also the same for both gases.

Now, $\begin{array}{rcl}\mathrm{molecular}\mathrm{mass}\mathrm{of}\mathrm{Hydrogen}{\mathrm{M}}_{\mathrm{H}}& =& 2{\mathrm{gmol}}^{-1},\\ \mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{Oxygen}{\mathrm{M}}_{\mathrm{O}}& =& 32{\mathrm{gmol}}^{-1},\end{array}$

Hence, $\begin{array}{rcl}\mathrm{velocity}\mathrm{of}\mathrm{sound}\mathrm{in}\mathrm{Hydrogen},\mathrm{vH}& =& \surd \mathrm{\gamma RT}/2\\ \mathrm{Velocity}\mathrm{of}\mathrm{sound}\mathrm{in}\mathrm{Oxygen},\mathrm{vO}& =& \surd \mathrm{\gamma RT}/32\\ \mathrm{Therefore},\mathrm{vO}/\mathrm{vH}& =& \surd 32/2\\ & =& 4/1\end{array}$

Final Answer: Therefore, option C $4:1$ is the correct option.