On this page
A diesel engine has no spark plug. It squeezes air so hard that the air becomes hot enough to ignite the fuel sprayed into it. That idea came from Rudolf Diesel, an engineer who set out to beat the steam engine using the thermodynamics you study in Class 11. This post covers his story, his patent, a worked compression calculation and the mistakes students make with it.
Who was Rudolf Diesel?
The Neue Deutsche Biographie, the standard German biographical dictionary, records that he was born in Paris on 18 March 1858 to a German family. After the battle of Sedan in 1870 the family had to leave for London, and the 12-year-old Diesel travelled alone to relatives in Augsburg to go to school. He studied mechanical engineering at the Technische Hochschule (technical college) in Munich from 1875 to 1879.
In 1878, in Carl Linde's lectures on thermodynamics, he heard how poor the steam engine was. The NDB entry says even the best steam engines turned only 10 to 12% of the heat in their coal into useful work. Linde also told the class that Sadi Carnot had described an ideal heat-engine cycle in 1824, but nobody had built an engine that followed it. Diesel decided to.
He worked in Linde's ice factory in Paris from 1880, then spent 1883 to 1889 on an engine using high-pressure ammonia vapour, which failed. Around 1890 he arrived at the new principle: use only air as the working substance, compress it very strongly, and inject the fuel afterwards.
What did his patent claim?
German patent DE 67207, filed on 28 February 1892 and published on 23 February 1893, is titled "Arbeitsverfahren und Ausführungsart für Verbrennungskraftmaschinen", a working method and design for combustion engines. It contrasts his method with existing engines, where a fuel-air mixture is compressed and then explodes, causing a sudden jump in pressure and temperature.
The patent's defining feature is that pressure and temperature are raised to roughly their maximum not by combustion, but before it, by mechanical compression of pure air. The fuel is then burned gradually during a set part of the expansion stroke.
How did the first engines perform?
Diesel described the development in a lecture to the Association of German Engineers at Kassel on 16 June 1897, published in English the same year as Diesel's Rational Heat Motor. He wrote that the first diagram, in 1893, came with violent explosions that destroyed the measuring indicator. Years of rebuilding followed at the Augsburg engine works. He said his process needed 30, 40 or 50 atmospheres to reach ignition temperature by compression.
A 20 horsepower engine was tested in early 1897, including by Professor Schröter of the Technical College of Munich on 17 February. Diesel multiplied four efficiencies to get the overall result: 1 x 0.50 x 0.72 x 0.74. Check it: 0.50 x 0.72 = 0.36, and 0.36 x 0.74 = 0.2664, or about 26.6%. (The printed translation says 26.66%, a small slip; your own calculation gives 26.64%.) Compare that with the 12 to 13% he quoted for the best large steam engines.
Worked example: how hot does compressed air get?
The current NCERT Class 11 Physics chapter 11, Thermodynamics (2026-27 reprint), gives the adiabatic relation for an ideal gas, PV^γ = constant, where γ = Cp/Cv. Combine it with PV = µRT and you get TV^(γ-1) = constant.
Use sample numbers: air at T1 = 300 K and P1 = 1 atm is compressed quickly to one-sixteenth of its volume. Take γ = 1.4 for air.
Temperature: T2 = T1 (V1/V2)^(γ-1) = 300 x 16^0.4.
16^0.4 = 2^1.6 ≈ 3.03, so T2 ≈ 300 x 3.03 ≈ 909 K, about 636 °C.
Pressure: P2 = P1 (V1/V2)^γ = 16^1.4 = 2^5.6 ≈ 48.5 atm.
Now compare a compression to one-eighth of the volume: T2 = 300 x 8^0.4 ≈ 300 x 2.30 ≈ 689 K, and P2 = 8^1.4 ≈ 18.4 atm. Doubling the compression ratio raises the final temperature by about 220 K. The 48.5 atm figure also falls in the 30 to 50 atmosphere range Diesel described.
Common mistakes to avoid:
Using degrees Celsius. The relation needs kelvin. Using 27 instead of 300 gives nonsense.
Mixing up the exponents. Temperature uses γ - 1; pressure uses γ.
Treating it as isothermal. A fast compression has no time to lose heat, which is why it is modelled as adiabatic. A real engine loses some heat, so real temperatures are a little lower.
For the efficiency side of the story, see our guide to heat engines and the Carnot cycle, and read about Sadi Carnot, whose ideal cycle Diesel was chasing.
How did his life end?
The NDB entry says Diesel sold his rights during a period of ill health, made poor investments, and returned to developing the engine after his patents expired in 1908. On the night of 29 to 30 September 1913 he was crossing from Antwerp to Harwich; when the ship arrived in England he was not on board.
What can a student learn from how Diesel worked?
Start from the theory. He began with Carnot's ideal and asked what a real engine would need.
Accept a workable compromise. He gave up the extreme pressures of the ideal cycle for 30 to 50 atmospheres.
Record failures as data. His lecture lists each stage of the engine's development, including the explosions.
Check the numbers yourself. Even a printed result can carry a slip.
If adiabatic and isothermal processes still feel alike, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Redo the worked example for a compression to one-twelfth of the volume, then check whether your temperature falls between the two answers above.
