Question

If the temperature is raised by $1K$ from $300K$ , the percentage change in the speed of sound in the gaseous mixture is [ $R=8.314Jmol^{- 1}K^{- 1}$ ]

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

Answer 1

Answer: (A)

$\text{0.167}\%$

Answer 2

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