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You turn Celsius into kelvin by adding 273.15, but why should temperature have a lowest point at all, and why there? William Thomson, later Lord Kelvin, asked a deeper question in 1848: can temperature be defined without depending on any particular substance? His first answer was not the scale you use today. This post covers both of his absolute scales, works through the numbers, and shows what a student can take from the way he worked.
Who was Lord Kelvin?
The MacTutor biography gives his dates as 26 June 1824, in Belfast, to 17 December 1907, near Largs in Scotland. He began attending Glasgow University at the age of 10, went on to Cambridge, and in 1846 became professor of natural philosophy, the old name for physics, at Glasgow. He was knighted in 1866 for his work on the transatlantic telegraph cable and made Baron Kelvin of Largs in 1892. The Kelvin is the river that runs through the grounds of Glasgow University.
What was wrong with ordinary thermometers?
In 1848 the most trusted standard was the air thermometer, which reads temperature from how air expands. In his paper On an Absolute Thermometric Scale, given to the Cambridge Philosophical Society in June 1848 and reprinted in volume 1 of his collected papers, Thomson pointed out that any such scale refers to "a specific body as the standard thermometric substance". It gives convenient reference points, not an absolute scale.
In a footnote he added that if air kept contracting at the same rate, its volume would reach nothing at −273° of the air thermometer, a point that "cannot be reached at any finite temperature, however low".
What was his first absolute scale?
His idea was to define temperature through an ideal heat engine, using Sadi Carnot's theory. On the new scale, he wrote, "a unit of heat descending from a body A at the temperature T° of this scale, to a body B at the temperature (T−1)°, would give out the same mechanical effect, whatever be the number T." Because it relies on an ideal engine rather than a material, he argued, it "may justly be termed an absolute scale".
This works because, as NCERT Class 11 Physics states, the efficiency of a Carnot engine is independent of the working substance. But Carnot's theory, as Thomson used it in 1848, treated heat as a fluid that is conserved. When he reprinted the paper in 1882 he added a note that it was "wholly founded on Carnot's uncorrected theory", and gave a formula linking his first scale, θ, to his later one, t:
θ = 100 × (log t − log 273) / (log 373 − log 273)
Worked example: comparing his two scales
Use the formula with t in kelvin, rounded as Thomson did.
Boiling water, t = 373: the top and bottom of the fraction are equal, so θ = 100.
Melting ice, t = 273: log t − log 273 = 0, so θ = 0.
Liquid nitrogen, t = 77: log 77 = 1.8865, log 273 = 2.4362, log 373 = 2.5717. So θ = 100 × (1.8865 − 2.4362) / (2.5717 − 2.4362) = 100 × (−0.5497 / 0.1355) ≈ −406.
As t approaches 0, log t heads to minus infinity, and so does θ.
On the first scale, absolute zero is infinitely far away. Equal steps on it correspond to equal ratios on the modern scale.
Where did the modern scale come from?
James Joule's experiments convinced Thomson that heat is a form of energy, and in 1854 he published a second absolute scale. In the same collected papers he explains that, from experiments with Joule, temperature on this scale differs from the air thermometer only "by the addition of a constant number, which we find to be about 273·7". Melting ice was 273.7 and boiling water 373.7. Today NCERT's chapter on thermal properties uses T = t + 273.15 and puts absolute zero at −273.15 °C. Under the current SI, the BIPM defines the kelvin by fixing the Boltzmann constant at exactly 1.380 649 × 10⁻²³ J/K.
Check it with an engine. NCERT gives Carnot efficiency as η = 1 − T₂/T₁. Between 100 °C and 0 °C, η = 1 − 273.15/373.15 ≈ 0.268, or about 27%. With Celsius you would get 1 − 0/100 = 1, a perfect engine, which the second law forbids.
Common mistakes:
Using Celsius in a ratio. Differences are the same size in °C and K; ratios are not.
Mixing 273 and 273.15. Use the value the question gives, and stay consistent.
Thinking absolute zero was measured. It was found by extrapolation and by theory; no experiment reaches it.
What can a student take from how Kelvin worked?
Ask what a definition depends on. He saw that every thermometer secretly relied on one substance, and looked for something that did not.
Correct yourself in public. He reprinted his 1848 paper with a note on its flawed basis rather than quietly dropping it.
Connect topics. A question about engines answered a question about thermometers.
For the people behind his ideas, read our profiles of Sadi Carnot and James Joule, then try our heat engine and Carnot cycle problems. If entropy and absolute temperature still feel abstract, the Fermi Concept Library covers every concept in physics with its own explanation.
Try this now: on Kelvin's first scale, what temperature would a freezer at 255 K read?
