Three speeds of a gas

You will write functions for the three speeds of a gas, and one that works backwards to the temperature.

The idea. For a gas of molar mass $M$, in kg/mol, at the kelvin temperature $T$:

• most probable speed $v_{mp} = \sqrt{2RT/M}$;
• average speed $v_{avg} = \sqrt{8RT/(\pi M)}$;
• rms speed $v_{rms} = \sqrt{3RT/M}$.

Your tasks.

1. In v_rms, return the rms speed in m/s.
2. In v_mp, return the most probable speed in m/s.
3. In v_avg, return the average speed in m/s.
4. In temperature_for, return the temperature at which a gas of molar mass M has the rms speed v.