Classical thermodynamics, heat transfer Definition

Thermodynamic temperature

Builds on Temperature Heat Reversible process Thermodynamic cycle

Definition

Let $\theta$ be an empirical temperature. Let two heat reservoirs have empirical temperatures $\theta_1 > \theta_2$ . Consider a reversible cycle that exchanges heat only with these two reservoirs. Let it absorb heat $Q_1 > 0$ from the first reservoir and give heat $Q_2 > 0$ to the second. By the second law, $Q_1 / Q_2 = \varphi(\theta_1) / \varphi(\theta_2)$ for a positive function $\varphi$ that does not depend on the cycle. The thermodynamic temperature is $T = c \, \varphi(\theta)$ , where the constant $c > 0$ fixes the unit.

Remarks

So $T$ is defined by the rule $T_1 / T_2 = Q_1 / Q_2$ for reversible cycles between two reservoirs. The unit is the kelvin; since 2019 the kelvin is fixed by setting the Boltzmann constant to $1.380649 \times 10^{-23}$ joule per kelvin. For an ideal gas, $T$ agrees with the ideal-gas temperature $pV/(nR)$ . The Celsius scale is not a thermodynamic temperature in this sense: $t_1 / t_2$ is not the heat ratio, and $t$ can be negative. For a system with internal energy $U$ and entropy $S$ , one has $T = (\partial U / \partial S)_{V, N}$ .

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Tag	`DG4ZP6XWDB`
URI	`m2://DG4ZP6XWDB`
Kind	definition
Writing	W0 stub
MSC	80A05, 80A10
Defines	Thermodynamic temperature
Uses	Temperature, Heat, Reversible process, Thermodynamic cycle
Changed	3 November 2026

Thermodynamic temperature

Definition

Remarks

Reading path

Further reading

What this page needs for W1

What links here