Question

If at same temperature and pressure, the densities for two diatomic gases are $d_1$ and $d_2$ respectively, then the ratio of velocities of sound in these gases will be

• A. $\sqrt{\frac{d_{2}}{2d_{1}}}$
• B. $\sqrt{\frac{d_{2}}{d_{1}}}$
• C. $\sqrt{\frac{2d_{1}}{d_{2}}}$
• D. $\sqrt{\frac{d_{1}}{d_{2}}}$

Answer 1

Answer: (B)

The velocity of sound in a gas is given by
$v=\sqrt{\frac{\gamma p}{d}}$ where $\gamma=\frac{C_{P}}{C_{V}}$
$p=$ pressure $\,\,\,\,\,\, d=$ density
$\therefore $ For two gases at constant pressure,
$\frac{v_{1}}{v_{2}}=\sqrt{\frac{d_{2} \gamma_{1}}{d_{1} \gamma_{2}}}$
For a diatomic gas $\gamma_{1}=\gamma_{2}=\frac{7}{5}$
$\therefore \frac{v_{ l }}{v_{2}}=\sqrt{\frac{d_{2}}{d_{1}}}$