Hello, I've made this sketch to illustrate what is going on inside the tank.
Imagine you have some gas at the bottom of it that expands to occupy all the volume while the rest of the gas is expelled from the tank.
The expanding gas is almost at the same pressure than the rest of the tank. It is also at the same temperature. This is a quasi eqilibrium situation. So you can calculate the expansion as being reversible and adiabatic.
If you do the numbers assuming ideal conditions that is, Cv is 3/2R for monoatimic gas, 5/2R for diatomic gas, Cp = CV + R and that the compressibility is 1 then the calculated temperatures are:
-96.5 °C for N2 and -129.9 °C for H2.
So yes, the lower temperaure of Helium has to do with the fact that it is monoatomic, and it has a lower heat capacity than a diatomic gas.
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If you do the rigorous calculation by simulating an adiabatic reversible expansion using a method like Refprop that account for non ideal behaviour you will have other temperatures, but Helium will be a lower temperature than Nitrogen.
There are other facts that determine what the final temperature would be:
- Heat transfer into the tank. Can be minimized with good insulation.
- Turbulence inside the bottle that dissipates as heat.
- Heat capacity of the tank itself. I would not ignore it, since the metal mass can be significant compared to the gas mass.
Regards