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The first law of thermodynamics is often taught as a formula, ΔU = Q − W. Behind it is a simpler idea: energy changes form but is not created or destroyed. One of the first people to state that idea in general terms was not a physicist but a ship's doctor. This post covers Julius Robert Mayer's story, checks his famous number, and shows what it means for your exam.
Who was Julius Robert Mayer?
His entry in the Neue Deutsche Biographie gives his dates as 25 November 1814 to 20 March 1878, both in Heilbronn. He studied medicine at Tübingen from 1832 to 1838. In February 1840 he sailed as ship's doctor on a Dutch three-masted ship bound for the East Indies, and in February 1841 he returned to Heilbronn, where he practised as a doctor.
What did he see in Java?
The NDB tells the story. In Batavia (now Jakarta) in June 1840, many of the crew fell ill with pneumonia, and Mayer let blood from their veins as doctors then did. The venous blood, normally dark because it carries little oxygen, was strikingly bright. Mayer knew Lavoisier's idea that body heat comes from oxidising food. He reasoned that in a hot climate the body needs to make less heat, so less oxygen is used and venous blood stays brighter.
The NDB is clear that this explanation was wrong; the colour has a different cause. But the question it raised was the right one. If heat, motion and chemical change are linked, there must be a fixed exchange rate between them.
What did his 1842 paper say?
His first manuscript, sent in June 1841 to the physics journal edited by Poggendorff, was ignored, and the NDB notes it contained errors. He rewrote it, and "Bemerkungen über die Kräfte der unbelebten Natur" (Remarks on the forces of inorganic nature) appeared in Liebig's Annalen der Chemie in 1842. He argued that the "forces" of nature, what we call forms of energy, change into one another while their quantity stays the same.
The paper ends with a number. In the English translation printed in Youmans' 1865 collection, taking the ratio of the specific heats of air at constant pressure and constant volume as 1.421, Mayer concludes "that the warming of a given weight of water from 0° to 1° C. corresponds to the fall of an equal weight from the height of about 365 metres." A footnote adds that with corrected data for air the number rises and agrees with Joule's experiments.
Worked example: checking the 365 metres
How far must 1 kg of water fall for its potential energy to equal the heat that warms it by 1 °C? The NCERT Class 11 chapter Thermodynamics gives the specific heat of water as 4186 J kg⁻¹ K⁻¹. Take g = 9.8 m s⁻².
Heat needed. Q = mcΔT = 1 × 4186 × 1 = 4186 J.
Set equal to mgh. 1 × 9.8 × h = 4186.
Solve. h = 4186 / 9.8 = 427 m.
Compare. Mayer's 365 m is about 15 per cent low. His method was sound; the input data for air were not accurate enough.
The same chapter gives the relation behind his method: for an ideal gas, Cp − Cv = R. The NCERT Kinetic Theory chapter lists Cv = 20.8 and Cp = 29.1 J mol⁻¹ K⁻¹ for a diatomic gas such as air. The difference, 8.3, matches R = 8.31, and the ratio 29.1 / 20.8 = 1.40 is close to Mayer's 1.421.
Which mistakes does this help you avoid?
Mixing calories and joules. NCERT gives 1 cal = 4.186 J. Convert before you compare heat with work.
Forgetting that Cp is larger than Cv. At constant pressure, some heat goes into work done by the expanding gas.
Sign errors in the first law. Decide whether W is work done by or on the gas, and keep to it. Our post on thermodynamics sign conventions shows both.
The JEE (Main) 2026 syllabus lists the first law of thermodynamics and specific heat capacities of gases. Check the current syllabus for your exam.
How was he recognised?
Slowly. The NDB describes how his 1845 follow-up, which extended the idea to electricity, magnetism, chemistry and living things, had to be printed at his own expense and was little read. James Joule's measurements from 1843 and Helmholtz's essay of 1847 carried the subject forward. Mayer also went through long periods of serious mental illness. Only after John Tyndall championed his work did recognition come, including the Royal Society's Copley Medal in 1871. Our post on James Joule and the mechanical equivalent of heat tells the experimental side.
What can a student take from Mayer's way of working?
Follow up odd observations. A strange colour of blood led him to a law of physics.
Put a number on an idea. His 365 m made the claim testable, even though it was off.
Use existing data cleverly. He extracted a new constant from measurements other people had made for a different purpose.
If energy bookkeeping in thermodynamics still confuses you, the Fermi Concept Library covers every concept in physics with its own lesson, so you can revise heat, work and internal energy one at a time.
Try it now: using 4186 J kg⁻¹ K⁻¹, find the temperature rise of water after falling 100 m, if all its potential energy becomes heat.
