thermodynamic temperature scale
Ordinary thermometers rely on a substance — the height of mercury, the swelling of alcohol — and different substances disagree slightly, so the 'degree' is a bit arbitrary. The thermodynamic temperature scale escapes that by defining temperature from a law of nature rather than from any material. It is temperature with no thermometer fluid baked in.
Kelvin's insight was that the ideal Carnot engine offers a substance-free ruler: the ratio of two temperatures equals the ratio of heat absorbed to heat rejected by a reversible engine running between them. Anchoring the scale at absolute zero — where, in principle, that heat ratio would vanish — fixes a true zero point. The result is the kelvin scale, where each degree matches a Celsius degree in size but the count starts from absolute zero (about −273.15 °C).
Why it matters: this is the temperature that belongs in every serious thermodynamic formula — the T dividing heat to give entropy, the T in the Carnot efficiency, the T in the gas laws. Because it has a genuine zero, ratios mean something: 200 K really is twice as hot, thermodynamically, as 100 K. The caveat: that statement is false on the Celsius or Fahrenheit scales, whose zeros are arbitrary, which is why those scales must never be used inside these equations.
Heating a gas from 20 °C to 40 °C does not double its tendency to expand, even though the Celsius number doubled. Convert to kelvin — 293 K to 313 K — and you see the real change is a mere 7%. The gas laws only behave when you feed them the thermodynamic temperature.
Only the kelvin scale has a true zero, so only its ratios are physically meaningful.
The thermodynamic scale and the ideal-gas scale turn out to be numerically identical, which is a lucky and deep coincidence — it lets us realize an abstract, engine-based definition with a practical gas thermometer.