THM-26

Carnot COP (fridge)

Reversible refrigerator.

Reading speed

GoverningCarnot COP (fridge)

Governing equation

COP=T_c/(T_h-T_c)

$Tc \in \left[200, 300\right]$

where

Tc: Tc (K)
Th: Th (K)
COP: Carnot COP (fridge) (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

COP=T_c/(T_h-T_c)

$Tc \in \left[200, 300\right]$

$Tc = 200$ $COP = 2$

Along the curve

②

Domain of the variable — blue

Tc_{\min} = 200,\quad Tc_{\max} = 300

$Tc \in \left[200, 300\right]$

$Tc = 200$ $Tc = 200$

Along the curve

③

Response curve — green

COP=T_c/(T_h-T_c)

$Tc \in \left[200, 300\right]$

$Tc = 200$ $COP = 2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}COP}{\mathrm{d}Tc}

$Tc \in \left[200, 300\right]$

$Tc = 200.6$ $COP^{\prime} = 0.03$

Along the curve

Lecture brief

Historical brief

Carnot (1824), Clausius entropy, the first law and later van der Waals and Gibbs potentials turned heat into a state science. The sheets compute work, efficiency and vapour pressure. This sheet (THM-26 — Carnot COP (fridge)) is the form associated with Carnot COP (fridge). Working symbols: $Tc$ , $Th$ $\rightarrow$ $COP$ . Reversible refrigerator. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

COP

from

Tc

Th

in Thermodynamics via

COP=T_c/(T_h-T_c)

Reversible refrigerator. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Tc = 260.000\,\mathrm{K}

Th = 300.000\,\mathrm{K}

, the governing relation

COP=T_c/(T_h-T_c)

yields

COP = 6.500\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Tc Tc260 KTh Th300 K

Outputs

Carnot COP (fridge) COP6.500 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Reversible refrigerator. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube