Question

By how many folds the temperature of a gas would increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from \(5\times10^{4}\) cm/s to \(10\times10^{4}\) cm/s ?

• A. Two
• B. Three
• C. Six
• D. Four

Hint:

Use \(u_{rms}=\sqrt{3RT/M}\), so \(T \propto u_{rms}^2\) for the same gas.

Answer 1

The Correct Option is D

Use kinetic energy: average translational energy per molecule \(\tfrac12 m\overline{u^2} = \tfrac32 kT\), so \(T\propto \overline{u^2}\).
The rms speed doubles, so \(\overline{u^2}\) becomes \(2^2 = 4\) times, and therefore T becomes 4 times.
Answer: (4) Four