Question

Velocity of sound in oxygen at $27{}^{\circ }C$ is double of that in helium at $T^{\circ }C$ then $T$ is

• A. $0.78{}^{\circ }C$
• B. $-265{}^{\circ }C$
• C. $-168{}^{\circ }C$
• D. $3{}^{\circ }C$

Answer 1

The correct option is B $-265{}^{\circ }C$

$V=\sqrt{\frac{\gamma RT}{M_0}}\Rightarrow V_{0_2}=\sqrt{\frac{7}{5}\frac{R\times 300}{32}}$

$V_{He}=\sqrt{\frac{5}{3}\frac{R\times T}{4}}\Rightarrow \frac{V_{0_2}}{V_{He}}=\sqrt{\frac{7\times 300\times 3\times 4}{5\times 32\times 5T}}$

$4=\frac{7\times 300\times 12}{25\times 32\times T}\Rightarrow T=7.87K$ or $T\approx -{265}^{\circ }C$