Question

Temperature of an ideal gas, initially at ${27}^{o}C$, is raised by $6^{o}C$. The rms velocity of the gas molecules will

• A. Increase by nearly $2$%
• B. Decrease by nearly $2$%
• C. Increase by nearly $1$%
• D. Decrease by nearly $1$%

Answer 1

The correct option is C Increase by nearly $1$%

RMS velocity of a gas is given by:

$v_{rms}=\sqrt{\frac{3RT}{M}}$

$v_{rms}\propto \sqrt{T}\Rightarrow \frac{\Delta v}{v}=\frac{1}{2}\frac{\Delta T}{T}=\frac{1}{2}\times \frac{6}{300}=\frac{1}{100}$
$\therefore$ RMS velocity of the gas increases by nearly $1$%