Question

If the ratio of the specific heats of He and $H_2$ are 5/3 and 7/5 respectively at the same temperature, what is the ratio of sound velocity in these gases ?

• A. $5:2$
• B. $2:5$
• C. $5:\sqrt{42}$
• D. $\sqrt{42}:5$

Answer 1

The correct option is C $5:\sqrt{42}$

since the speed of sound in gases is directional proportional to square root of ratio of specific heats and invertionally proportional to square root of density.

so ,

$\frac{V_{He}}{V_{H_2}}=\frac{\sqrt{\frac{5}{3}}}{\sqrt{\frac{7}{5}}}=\frac{5}{\sqrt{42}}$