Thermican: Bolometer Time Constant

Thermodynamics & Statistical Physics arc, page 57 of 193. Back to The Pixelated Physics Universe

Who they are

Thermican has one line, and says it often: “Τ = c/g. slow to warm, slow to forgive.”

Thermican 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

A bolometer with heat capacity C and thermal link G has time constant τ = C/G; it warms and cools exponentially with τ, just like Newton's law of cooling: ΔT = ΔT0 e−t/τ, where ΔT is the temperature difference to the room, ΔT0 its initial value, t the time and τ the time constant.

$$ \begin{gathered} \tau = \frac{C}{G} \\ \Delta T = \Delta T_0\, e^{-t/\tau} \end{gathered} $$

Symbol Meaning SI unit
$\tau$ thermal time constant s
$C$ heat capacity of the bolometer J/K
$G$ thermal conductance of the link to the bath W/K
$\Delta T$ temperature difference to the surroundings K
$\Delta T_0$ initial temperature difference (t = 0) K
$t$ time s

Sources

Crossovers

Thermican meets Tepidora (Zeroth Law of Thermodynamics). 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.

Thermican meets Phaselocke (Lock-In Amplifier). Thermican's slow time constant limits how fast her bolometer can respond. Phaselocke chops the signal at a frequency she can follow and pulls it out of the drift with a lock-in.

Thermican meets Boundraith (Kapitza Resistance). Thermican's bolometer needs a weak thermal link G to its bath. Boundraith's boundary resistance is one of the things that sets that link at millikelvin temperatures.

Wear the lore

Concept keywords: Bolometer Time Constant, Thermican, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics