THM-03

Clausius entropy (reversible heat)

ΔS = Qrev / T for a reservoir exchange.

Reading speed

EntropyClausius 1865

Governing equation

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

where

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

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

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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