Ideal Gas Law (PV = nRT)
Leave any one of P, V, n, T blank — the card solves for it.
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The engineering
The workhorse equation of state, in kPa·L·mol·K so R is 8.3145 and no unit gymnastics are needed. Temperature must be absolute — the kelvin field is deliberate, because plugging °C into a gas law is the classic process-engineering error. One mole at 0 °C and 101.325 kPa occupies 22.414 L; that pair makes a good self-check.
Ideal means: molecules with no volume and no attraction. It holds within a percent or two for common gases near ambient conditions, and drifts badly at high pressure (above ~10 bar start asking questions), near condensation, or for strongly polar vapors — that is compressibility-factor and cubic-equation territory.
Where this math comes from
The law was assembled over 170 years by four hands: Robert Boyle (1662) found PV constant at fixed temperature, Gay-Lussac published the temperature law in 1802 (crediting Jacques Charles's unpublished work), and Amedeo Avogadro proposed in 1811 that equal volumes hold equal numbers of molecules — a claim ignored for half a century.
Émile Clapeyron combined the pieces into a single equation of state in 1834 while working on Carnot's theory. The universal constant R fell out once Avogadro was finally believed (after Cannizzaro's 1860 campaign), and the ideal gas became thermodynamics' favorite reference substance — the gas all real gases are judged against.
- 1662Robert BoylePV = constant at fixed temperature.
- 1802Joseph Gay-LussacVolume–temperature law published (crediting Charles).
- 1811Amedeo AvogadroEqual volumes, equal molecules — n enters the equation.
- 1834Émile ClapeyronCombines the laws into PV = nRT.
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