Question

If velocity of sound in O₂ gas at absolute temperature T is V, if temperature becomes double the molecular oxygen gas dissociates into atomic form, then the new velocity of sound in atomic oxygen is –

• A. V
• B. 2 V
• C. $\frac{5}{\sqrt{3}}$V
• D. $\frac{10V}{\sqrt{21}}$

Answer 1

Answer: (D)

$\frac{10V}{\sqrt{21}}$

Answer 2

v = $\sqrt{\frac{\gamma RT}{M_{\omega}}}$ = $\sqrt{\frac{7}{5} \times \frac{RT}{32}}$,v¢ = $\sqrt{\frac{5}{3} \times \frac{R(2T)}{16}}$

$\frac{v'}{v}$ = $\sqrt{\frac{5 \times 2T \times 5 \times 32}{3(16)\mspace{6mu}\mspace{6mu} 7 \times T}}$= $\frac{5 \times 2}{\sqrt{21}}$, v¢ = $\frac{10}{\sqrt{21}}$ v