Almost all gases cool down when expanded at a throttle (or during free expansion). This phenomenon is particularly striking with whipped cream dispensers: the cartridge screwed in becomes so cold due to the expansion of the pressurised gas that contact can even cause frostbite.
The temperature change after the throttle occurs because* the average distance between individual molecules increases during expansion, so a certain amount of work is done against the intermolecular attractive forces, ultimately removing thermal energy from the gas.
With hydrogen and a few other gases, however, the exact opposite happens: the gas warms up when expanded at a throttle. From a thermodynamic perspective, such a throttle represents an isenthalpic expansion, since in this type of process the sum of the internal energy U and the product of volume V and pressure p does not change.
Crucial for calculating the temperature rise under real conditions is the Joule-Thomson coefficient, which reverses sign at a certain temperature. This so-called inversion temperature lies for hydrogen (at atmospheric pressure) at approximately -73°C (≈ 200 K). For air, for example, the inversion temperature is around 350–490°C depending on composition, meaning that air also continues to warm up during throttling at very high temperatures. At the particle level, one can say that above this temperature the molecules tend to repel each other anyway, which is why an increase in distance due to expansion accelerates them rather than slowing them down.
The following calculator processes the inputs "Initial temperature" (before the throttle), "Initial pressure" (before the throttle) and "Final pressure" (after the throttle). Real gas conditions are applied so that the most accurate values possible are always output.
Note: In practice, energy is dissipated to the surroundings (e.g. through pipe walls), which means the temperature rise of the gas may be somewhat lower than the calculated value.
*Note: A temperature change also occurs during compression or expansion in a piston, for both real and ideal gases. However, this has a different cause and is not a Joule-Thomson effect.
Note: In an ideal gas the Joule-Thomson effect cannot be observed.
Note: The accuracy of the final temperature depends on the given starting temperature. The highest accuracy is achieved under standard conditions (20°C).
All online tools have been programmed to the best of my knowledge; however, errors cannot be entirely excluded. Any use is therefore at your own risk. Any legal or financial claims are excluded.