Question

A helium atom has a mass of 6.7 × 10^-27 kg. If a sample of gas has a root mean square speed of 500 m s^-1, calculate the temperature of the gas.

Answer 1

We can find the root mean square speed as follows:

$$v_{rms}=\sqrt{\dfrac{3RT}{M}}.$$

From this formula we can find the temperature of the gas:

$$T=\dfrac{v_{rms}^2M}{3R},$$ $$T=\dfrac{(500\ \dfrac{m}{s})^2\cdot4\cdot10^{-3}\ \dfrac{kg}{mol}}{3\cdot8.314\ \dfrac{J}{K\cdot mol}}=40.1\ K.$$