Almost all gases become colder when they expand at a throttle point (or expansion). This phenomenon becomes particularly clear, for example, when using a capsule cream dispenser: here, the screwed-in capsule becomes so cold due to the expansion of the compressed gas that freezing fires can even occur during use.
The change in temperature after the throttle is caused by the fact* that the mean particle distance of the individual molecules increases during expansion, so a certain effort is made against the molecular forces of attraction, which ultimately removes heat energy from the gas.
In the case of hydrogen and a few other gases, however, the exact opposite happens: the gas heats up when it expands at a throttle point. From a thermodynamic point of view, such a throttle represents isenthalpic expansion, as the sum of the internal energy U and the product of volume V and pressure p does not change in this type of process.
The Joule-Thomsen coefficient, which is inverted above a certain temperature, is particularly important for calculating the temperature increase under real conditions. This so-called inversion temperature is approximately -80°C for hydrogen. For air, for example, the inversion temperature corresponds to around 450°C, which means that air also heats up further at high temperatures when it expands. At the particle level, it can be said that the molecules would tend to repel each other above this temperature anyway, which means that more work is done by the particle interactions during expansion than is added.
The following computer processes the inputs "Starting temperature" (before the throttle), "Starting pressure" (before the throttle) and "Final pressure" (after the throttle). The calculation is performed under real conditions so that the values output are always as exact as possible.
Note: In the real case, energy is released into the environment (e.g. through pipe walls), so the temperature rise of the gas may be lower than calculated here.
*Note: A temperature change also occurs in real and ideal gases during compression or expansion, e.g. in the piston. However, this has nothing to do with the Joule-Thomson effect, but with the volume work performed. In particular, the superposition of these two effects (volume work and Joule-Thomson effect) causes computational difficulties in complex systems (such as a filling station).
Note: Ideal Gases do not show JT Effects.
Note: The accuracy of the final temperature depends on the given start temperature. The highest accuracy is achieved under standard conditions (20°C), from approx. -40°C - +60°C the accuracy of the calculation is only approx. +/- 2%.
I have programmed all online tools to the best of my knowledge and belief, but errors can of course still not be ruled out. Any use is therefore at your own risk. Any legal or recourse claims are excluded.