THM-03

Clausius entropy (reversible heat)

ΔS = Qrev / T for a reservoir exchange.

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EntropyClausius 1865

Governing equation

\Delta S = \dfrac{Q_{\mathrm{rev}}}{T}

$T \in \left[50, 2000\right]$

where

Q_{\mathrm{rev}}: Reversible heat (kJ)
T: Temperature (K)
\Delta S: Entropy change (kJ/K)

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

\Delta S = \dfrac{Q_{\mathrm{rev}}}{T}

$T \in \left[50, 2000\right]$

$T = 50$ $\Delta S = 0.4$

Along the curve

②

Domain of the variable — blue

T_{\min} = 50,\quad T_{\max} = 2000

$T \in \left[50, 2000\right]$

$T = 50$ $T = 50$

Along the curve

③

Response curve — green

\Delta S = \dfrac{Q_{\mathrm{rev}}}{T}

$T \in \left[50, 2000\right]$

$T = 50$ $\Delta S = 0.4$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta S}{\mathrm{d}T}

$T \in \left[50, 2000\right]$

$T = 62.26$ $\Delta S^{\prime} = -0.005$

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-03 — Clausius entropy (reversible heat)) is the form associated with Clausius 1865. Working symbols: $Q_{\mathrm{rev}}$ , $T$ $\rightarrow$ $\Delta S$ . Clausius defined dS = đQrev / T so that ∮ đQ/T ≤ 0, with equality for reversible cycles.

Purpose

Purpose: compute

\Delta S

from

Q_{\mathrm{rev}}

T

in Thermodynamics via

\Delta S = \dfrac{Q_{\mathrm{rev}}}{T}

ΔS = Qrev / T for a reservoir exchange. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Q_{\mathrm{rev}} = 20.000\,\mathrm{kJ}

T = 300.000\,\mathrm{K}

, the governing relation

\Delta S = \dfrac{Q_{\mathrm{rev}}}{T}

yields

\Delta S = 0.0667\,\mathrm{kJ/K}

. Isothermal reversible transfer with a single T. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Reversible heat Q_{\mathrm{rev}}20 kJTemperature T300 K

Outputs

Entropy change \Delta S0.0667 kJ/K

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Narration of this film

Isothermal reversible transfer with a single T.

Clausius defined dS = đQrev / T so that ∮ đQ/T ≤ 0, with equality for reversible cycles.

Reading speed

Watch on YouTube