How this instrument works
The ideal gas law, PV = nRT, links four measurable quantities through one constant. Solved for temperature, it reads T = PV ⁄ (nR): multiply pressure by volume, then divide by the amount of gas and the molar gas constant. Physically, that product PV behaves like an energy — pressure is force per area, volume is a length cubed, and force times length is work — so dividing that energy-like quantity by n·R converts it into the temperature scale kinetic theory predicts.
R itself is not arbitrary. It is a constant that makes the average translational kinetic energy of gas molecules equal to (3/2)kT per particle, scaled up from one molecule to one mole via Avogadro's number. Since the 2019 SI redefinition, R = 8.314462618 J·mol⁻¹K⁻¹ is fixed exactly, because the Boltzmann constant k and Avogadro's number were themselves fixed by definition. Nothing about R is measured anymore — it is arithmetic on two defined constants.
The formula assumes an ideal gas: point-like molecules with no volume of their own and no forces between them except during collisions. Real gases only approximate this. Air at room temperature and pressure tracks it within a fraction of a percent, which is why the law is trusted for everyday engineering, but compress a gas hard or chill it toward its condensation point and molecules' own size and mutual attraction start pulling the real temperature away from what T = PV ⁄ (nR) predicts.
- Enter Pressure — the units menu offers Pa, kPa, or atm. Standard atmospheric pressure is 101.325 kPa.
- Enter Volume — choose ml, l, or m³: gas volume actually occupied, not a container's rated capacity.
- Set Amount, mol to the quantity of gas present, in moles. It must be greater than zero.
- Read Temperature, K — the instrument solves T = PV ⁄ (nR) and reports kelvin to six decimal places.
- Leaving Amount, mol at zero or below triggers a warning instead of a result, since dividing by zero moles is undefined.
Worked example — one mole at the historical STP volume
Take one mole of an ideal gas, n = 1 mol, held at standard atmospheric pressure, P = 101.325 kPa, which is 101,325 Pa, and let it occupy exactly 22.414 litres, or 0.022414 m³ — the molar volume every introductory chemistry course quotes for standard temperature and pressure. Solving T = PV ⁄ (nR) gives T = (101,325 Pa × 0.022414 m³) ⁄ (1 mol × 8.314462618 J·mol⁻¹K⁻¹) = 273.150371 K.
That result is not a coincidence: 273.150371 K sits within four ten-thousandths of a kelvin of 273.15 K, the exactly-defined ice point of water, 0 °C. That tiny gap exists because 22.414 L/mol is itself a rounded figure — the molar volume that follows exactly from 101.325 kPa, 273.15 K, and today's fixed R works out to 22.413969… litres, agreeing with 22.414 only to five significant figures.
A chemistry instructor runs this same arithmetic backward to check whether a gas sample truly sits at standard conditions before a titration; a process engineer does it to infer a stored gas's temperature from a pressure gauge and a cylinder's calibrated volume, without opening the valve to measure it directly.
Questions
What is the ideal gas law rearranged to solve for temperature?
It is PV = nRT solved for T, giving T = PV ⁄ (nR). Given pressure, volume, and amount of gas, temperature follows by algebra alone, assuming that gas behaves ideally — point-sized molecules with no forces between them except during a collision.
Why does 22.414 litres per mole appear in the example?
It is the historical, pre-1982 standard molar volume: at 101.325 kPa and 0 °C, one mole of an ideal gas occupies 22.414 L. Older textbooks and gas tables still use it, though today's IUPAC standard state, 100 kPa and 0 °C, gives 22.711 L ⁄ mol instead — check which STP a source means before comparing figures.
What happens if Amount, mol is set to zero?
The calculator withholds a result rather than dividing by zero. Its built-in check reports 'Amount of gas must be greater than zero.' Physically, zero moles means no gas is present, so no temperature is defined — the law describes a substance, not empty space.
Does this formula still work for real gases like air or nitrogen?
Closely, at ordinary conditions — air tracks the ideal gas law within about a tenth of a percent near room temperature and pressure. Agreement worsens as pressure rises or temperature drops toward condensation, where molecular size and intermolecular attraction matter; a real-gas equation of state such as van der Waals handles that regime better.
Can Pressure be zero?
Yes, and it drives the computed temperature to zero as well, for any fixed volume and amount — a boundary case this instrument's own test suite checks directly. It is a mathematical limit rather than a physical one: no real gas reaches absolute zero, let alone at zero pressure.
Why does the result show six decimal places?
Because this site verifies every formula against exact reference values, and near standard conditions small input changes shift its last digits. Six decimals let you confirm the calculator reproduces a known figure — 273.150371 K for one mole at 101.325 kPa in 22.414 L — to the final place.