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Industrial oxygen, nitrogen and argon are separated from air that has been cooled until it turns liquid. The method that made this possible on a factory scale came from Carl von Linde, an engineering professor who started out building refrigerators for beer. His key idea was to take a cooling effect everyone thought was too small to matter and make it add up. This post covers his life, the physics, a worked example, and what students can learn from his approach.
Who was Carl von Linde?
The Neue Deutsche Biographie, the standard German national biography, gives his life in detail. He was born on 11 June 1842 at Berndorf near Kulmbach in Bavaria and died in Munich on 16 November 1934. The son of a pastor, he chose engineering after seeing the steam engines in a cotton mill as a schoolboy. He studied at the Polytechnikum in Zurich, where Rudolf Clausius taught physics, and became a professor of theoretical mechanical engineering in Munich in 1868, with a full chair from 1871.
How did brewing lead him to refrigeration?
According to the NDB, Linde studied the refrigerating machines of his day in 1871 and judged their efficiency inadequate. He favoured compressing the vapour of a volatile liquid, removing the heat of compression, then letting the liquid expand through a throttle valve and evaporate, drawing heat from its surroundings. With money from Gabriel Sedlmayr of Munich's Spaten brewery he built an improved compression machine, patented in Bavaria in 1873. A second design, using ammonia from 1875, was patented in 1877.
In 1879 he founded the Gesellschaft für Linde's Eismaschinen with five partners, one of them a brewer who saw the value for beer making, as Linde's company history records. By 1890, the NDB says, more than 1,000 of his machines were working worldwide, almost two thirds in breweries.
How did Linde liquefy air?
When a real gas at high pressure is let out through a valve into a low-pressure space without doing outside work, it cools slightly. This is the Joule-Thomson effect. The NDB puts it at roughly 0.25 °C per atmosphere of pressure drop for air, a change engineers saw as too small to be useful.
Linde's answer, described in his US patent 727,650, filed in 1895 and granted in 1903, was a counter-current exchanger: two long coiled pipes, one inside the other, wrapped in insulation such as sheep's wool. High-pressure air flows down the inner pipe and through the valve. The cooled, expanded air flows back up the outer channel and pre-cools the incoming air. Each pass starts colder than the last, so the effect builds up until some air turns liquid. The NDB says his first apparatus made 3 litres of liquid air an hour, and the German patent DRP 88824 was granted in 1895.
Worked example: why one pass is not enough
Use the NDB figure of 0.25 °C per atmosphere, and a sample pressure drop from 200 atm to 1 atm.
Pressure drop. 200 − 1 = 199 atm.
Cooling in one pass. 199 × 0.25 ≈ 50 °C. Starting at 20 °C (293 K), the gas leaves at about −30 °C (243 K).
Target. Nitrogen boils at 77.3 K at atmospheric pressure, according to the NIST Chemistry WebBook. From 293 K that is a drop of 293 − 77 = 216 K.
Gap. One pass gives about 50 K of the 216 K needed, less than a quarter.
Counter-current fix. If the returning cold gas pre-cools the next batch to 243 K before the valve, that batch leaves near 193 K, and the next one colder still. The drops stack up over many cycles.
This is a simplified picture; the real cooling per atmosphere changes with temperature. The main lesson holds: a small effect, repeated with feedback, reaches a large result.
What mistakes do students make here?
Expecting an ideal gas to cool. In the ideal gas model, a gas pushed through a valve like this does not change temperature. Joule-Thomson cooling comes from the attractions between real molecules. Our post on real gases and the van der Waals equation explains those attractions.
Mixing Celsius changes and kelvin values. A change of 1 °C equals a change of 1 K, but temperatures in gas laws must be in kelvin.
Confusing a refrigerator with a liquefier. A refrigerator moves heat to keep something cold; a liquefier must take the gas below its boiling point. Our post on refrigerators and heat pumps covers the first.
If the counter-current loop is hard to picture from a description, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
What can you take from how Linde worked?
Start from a real customer. Breweries needed reliable cold, and their money paid for his machines.
Do the theory first. He judged existing machines by their efficiency before designing a better one.
Make small effects add up. His insight was the feedback loop, not a new law of physics.
Give credit where it is due. He did not claim the counter-current idea once he learned Siemens had described it.
Practice routine: redo the worked example for a drop from 100 atm to 1 atm, then estimate how many passes it would take to cool from 293 K to 77 K if every pass added the same drop.
Next step: write one paragraph explaining to a friend why a gas cools when it expands through a valve, using the word "attraction".
