Tepidora: Zeroth Law of Thermodynamics

Thermodynamics & Statistical Physics arc, page 49 of 193. Back to The Pixelated Physics Universe

Who they are

Tepidora has one line, and says it often: “Cold coffee. zeroth law achieved.”

Tepidora is a character of the Thermodynamics & Statistical Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

Zeroth law: systems in thermal equilibrium with a third are in equilibrium with each other; a forgotten mug reaches room temperature.

$$ \begin{gathered} T_A = T_C \ \wedge\ T_B = T_C \;\Rightarrow\; T_A = T_B \end{gathered} $$

Symbol Meaning SI unit
$T_A, T_B, T_C$ temperatures of systems A, B, C K

Sources

  • R. H. Fowler & E. A. Guggenheim, Statistical Thermodynamics (Cambridge, 1939)

Crossovers

Tepidora meets Creamward (Newton's Law of Cooling). Tepidora knows any mug ends at room temperature. Creamward races her there with Newton's law of cooling: the loss rate is proportional to the temperature difference, so the mug cools fast at first and slowly at the end.

Tepidora meets Thermican (Bolometer Time Constant). Thermican's bolometer and Tepidora's forgotten mug follow the same exponential approach to the bath temperature. For the bolometer the time constant is τ = C/G.

Tepidora meets Endoreva (Curzon Ahlborn Efficiency). Endoreva runs an engine between a hot and a cold reservoir at maximum power, with efficiency 1 − √(T_c/T_h). Tepidora warns that once the reservoirs reach the same temperature, the efficiency is zero and no engine works at all.

Wear the lore

Concept keywords: Zeroth Law of Thermodynamics, Tepidora, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics