Question

If the temperature is raised by $1K$ from $300K$ the percentage change in the speed of sound in the gaseous mixture is $\left(R=8.31 \quad J \quad mol ^{-1} \quad K ^{-1}\right)$ .

• A. $0.167\%$
• B. $0.334\%$
• C. $1\%$
• D. $2\%$

Answer 1

Answer: (A)

From, $v=\sqrt{\frac{\gamma R T}{M}}$
$\frac{\Delta v}{v}=\frac{1}{2}\frac{\Delta T}{T}$
$\frac{\Delta v}{v}\times 100=\frac{1}{2}\left(\frac{\Delta T}{T}\right)\times 100$
$=\frac{1}{2}\times \frac{1}{300}\times 100=0.167\%$