THM-05

Antoine saturation pressure

log10 Psat = A − B/(T+C).

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Phase changeAntoine 1888

Governing equation

\log_{10}P_{\mathrm{sat}}=A-\dfrac{B}{T+C}

$T \in \left[0, 180\right]$

where

A: A (—)
B: B (—)
C: C (—)
T: Temperature (°C)
P_{\mathrm{sat}}: Saturation pressure (kPa)

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

\log_{10}P_{\mathrm{sat}}=A-\dfrac{B}{T+C}

$T \in \left[0, 180\right]$

$T = 0$ $P_{\mathrm{sat}} = 0.606$

Along the curve

②

Domain of the variable — blue

T_{\min} = 0,\quad T_{\max} = 180

$T \in \left[0, 180\right]$

$T = 0$ $T = 0$

Along the curve

③

Response curve — green

\log_{10}P_{\mathrm{sat}}=A-\dfrac{B}{T+C}

$T \in \left[0, 180\right]$

$T = 0$ $P_{\mathrm{sat}} = 0.606$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P_{\mathrm{sat}}}{\mathrm{d}T}

$T \in \left[0, 180\right]$

$T = 1.132$ $P_{\mathrm{sat}}^{\prime} = 0.048$

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-05 — Antoine saturation pressure) is the form associated with Antoine 1888. Working symbols: $A$ , $B$ , $C$ , $T$ $\rightarrow$ $P_{\mathrm{sat}}$ . A three-parameter empirical integral of Clausius–Clapeyron, standard for vapour-pressure tables.

Purpose

Purpose: compute

P_{\mathrm{sat}}

from

A

B

C

T

in Thermodynamics via

\log_{10}P_{\mathrm{sat}}=A-\dfrac{B}{T+C}

log10 Psat = A − B/(T+C). Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 8.071\,\mathrm{—}

B = 1730.630\,\mathrm{—}

C = 233.426\,\mathrm{—}

T = 60.000\,\mathrm{^{\circ}C}

, the governing relation

\log_{10}P_{\mathrm{sat}}=A-\dfrac{B}{T+C}

yields

P_{\mathrm{sat}} = 19.870\,\mathrm{kPa}

. T in °C, P in mmHg, water-like constants. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

A A8.07131 —B B1730.63 —C C233.426 —Temperature T60 °C

Outputs

Saturation pressure P_{\mathrm{sat}}19.870 kPa

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Narration of this film

T in °C, P in mmHg, water-like constants.

A three-parameter empirical integral of Clausius–Clapeyron, standard for vapour-pressure tables.

Reading speed

Watch on YouTube