THM-22

Clausius–Clapeyron

Vapour pressure from a latent heat.

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GoverningClausius–Clapeyron

Governing equation

\ln(p_2/p_1)=-\Delta H/R(1/T_2-1/T_1)

where

p1: p1 (kPa)
T1: T1 (K)
T2: T2 (K)
dH: dH (kJ/mol)
p2: Clausius–Clapeyron (kPa)

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-22 — Clausius–Clapeyron) is the form associated with Clausius–Clapeyron. Working symbols: $p1$ , $T1$ , $T2$ , $dH$ $\rightarrow$ $p2$ . Vapour pressure from a latent heat. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

p2

from

p1

T1

T2

dH

in Thermodynamics via

\ln(p_2/p_1)=-\Delta H/R(1/T_2-1/T_1)

Vapour pressure from a latent heat. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

p1 = 101.000\,\mathrm{kPa}

T1 = 373.000\,\mathrm{K}

T2 = 353.000\,\mathrm{K}

dH = 40.700\,\mathrm{kJ/mol}

, the governing relation

\ln(p_2/p_1)=-\Delta H/R(1/T_2-1/T_1)

yields

p2 = 48.016\,\mathrm{kPa}

. 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

p1 p1101 kPaT1 T1373 KT2 T2353 KdH dH40.7 kJ/mol

Outputs

Clausius–Clapeyron p248.016 kPa

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Narration of this film

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

Vapour pressure from a latent heat. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube