Adiabatic Nozzle Expansion Spectroscopy

A recently discovered way to simplify complex electromagnetic spectra of molecules is to sweep a high-pressure stream of He gas across the sample and carry it to exit into the sample chamber of a spectrometer at a much lower pressure (nominally 1 atm) whereupon the He and the sample will drastically cool and this innovation in spectroscopy has resulted in some remarkably sharp spectral details being resolved in otherwise broad spectral blurs at room temperature. However, the He must be precooled to below 51°K, which is its Joule-Thomson inversion temperature. For simplicity we can consider N2 gas to illustrate the same point. 

Consider the expansion of 100 mL of N2 gas at 100 atm in a gas bottle at 30°C to 1 atm of pressure through a nozzle so rapidly as to achieve an adiabatic process. What is the temperature of the expanded N2 if the final volume is 10 L  

This rapid adiabatic expansion is sufficient to cool the nitrogen to below its boiling point of 77°K, so this is a way to make liquid nitrogen. There is a temperature for each gas called the Joule-Thomson inversion temperature and cooling occurs if the initial temperature is below that temperature but the gas heats upon expansion if the initial temperature is above the inversion temperature. At room temperature He is above its inversion temperature and will actually heat up upon expansion. Although there is also a pressure effect, there are absolute temperatures for this effect. For He the temperature is 51°K, for H2 202°K, for N2 621°K, and for O2 it is 764°K (see discussion at http //en.citizendium.org/wiki/Joule-Thomson effect). Thus, air (N2 + O2) can be liquefied by adiabatic expansion starting from room temperature and 1 atm, but He and H2 must be precooled to below their Joule-Thomson inversion temperatures. 

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