Question

The temperature of a gas is raised from ${27}^{o}C$ to ${927}^{o}C$. The root mean square speed

• A. Gets halved
• B. Gets doubled
• C. Is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
• D. Remains the same

Answer 1

Answer: (B)

Gets doubled

Given, $T_1={27}^{o}C=300K$
$T_2={927}^{o}C=1200K$
$v_{rms}=\sqrt{\left(\frac{3kT}{m}\right)}$
$\Rightarrow v_{rms}\propto \sqrt{T}$
$\therefore \frac{{\left(v_{rms}\right)}_1}{{\left(v_{rms}\right)}_2}=\sqrt{\frac{T_1}{T_2}}$
$\frac{{\left(v_{rms}\right)}_1}{{\left(v_{rms}\right)}_2}=\sqrt{\frac{300}{1200}}=\frac{1}{2}$
$\Rightarrow {\left(v_{rms}\right)}_2=2{\left(v_{rms}\right)}_1$