Question

The temperature of the ideal gas is increased from $27^{\circ }C$ to $927^{\circ }C$. The root mean square speed of its molecules becomes

• A. half
• B. twice
• C. four times
• D. one- fourth

Answer 1

Answer: (A)

Root mean square velocity $\left(v_{rms}\right)$ of an ideal gas at temperature $T$ is
$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$
Given, $T_1=27^{\circ }C$
$=273+27=300K$,
$T_2=927^{\circ }C$
$T_2=927+273=1200K$
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{300}{1200}}=\frac{1}{2}$
Hence, root mean square velocity will become double.