THM-07

Ideal-gas law

P V = n R T.

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Equations of stateClapeyron 1834

Governing equation

PV=nRT

where

n: Amount (mol)
T: Temperature (K)
V: Volume (L)
P: Pressure (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-07 — Ideal-gas law) is the form associated with Clapeyron 1834. Working symbols: $n$ , $T$ , $V$ $\rightarrow$ $P$ . Combining Boyle, Charles and Avogadro, Clapeyron wrote P V = n R T, the thermal equation of state of a dilute gas.

Purpose

Purpose: compute

P

from

n

T

V

in Thermodynamics via

PV=nRT

P V = n R T. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

n = 1.000\,\mathrm{mol}

T = 298.000\,\mathrm{K}

V = 24.500\,\mathrm{L}

, the governing relation

PV=nRT

yields

P = 101.125\,\mathrm{kPa}

. Dilute gas, R = 8.314 J/(mol·K). Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Amount n1 molTemperature T298 KVolume V24.5 L

Outputs

Pressure P101.125 kPa

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Narration of this film

Dilute gas, R = 8.314 J/(mol·K).

Combining Boyle, Charles and Avogadro, Clapeyron wrote P V = n R T, the thermal equation of state of a dilute gas.

Reading speed

Watch on YouTube