Question

The radio of the velocity of sound in Hydrogen gas $(\gamma =7/5)$ to that in Helium gas $(\gamma =5/3)$ at the same temperature is $\frac{\sqrt{21}}{5}$.

• A. True
• B. False

Answer 1

The correct option is B False

$\nu =\sqrt{\frac{\gamma RT}{M}}$

${\gamma }_H=\frac{7}{5};$ $M_H=1$

${\gamma }_{He}=\frac{5}{3};$ $M_{He}=1$

Temperature $=T$

$\therefore \frac{{\nu }_H}{{\nu }_{He}}=\sqrt{\frac{{\gamma }_H}{{\gamma }_{He}}\times \frac{M_{He}}{M_H}}=\sqrt{\frac{7}{5}\times \frac{3}{5}\times \frac{4}{1}}=\frac{84}{25}$

So the given statement is false.