Лаборатория идеального газа
Скачущие молекулы, настоящая физика: давление возникает из ударов о стенки, а P·V = n·R·T выполняется в реальном времени.
Это настоящая молекулярная динамика — никакого имитированного давления. Частицы летают и упруго отскакивают от стенок, а давление измеряется по импульсу, который они передают стенкам (оно совпадает с теоретическим N·k_B·T/A). Нагрейте газ, чтобы молекулы стали быстрее, перетащите поршень, чтобы изменить объём, добавьте частицы и смотрите, как P·V = n·R·T остаётся в равновесии при R = 8,314 Дж/(моль·К).
Пресеты
Показания
Формулы и источники
P·V = n·R·T (R = 8.314 J/mol·K)
P from wall-collision impulse (measured)
½m⟨v²⟩ ∝ T (kinetic theory)
Boyle P∝1/V · Charles V∝T · Gay-Lussac P∝T
The units and constants behind this gas
pV = nRT carries four units at once — pascal, litre, kelvin and mole. Since 2019 the gas constant R is not measured at all: it is the product of two numbers the SI fixes by definition.
Where R comes from
- R = 8.314462618 J mol⁻¹ K⁻¹ Molar gas constant · exact, because R = N_A · k_B and both of those are fixed by definition
- N_A = 6.02214076 × 10²³ mol⁻¹ Avogadro constant · defines the mole — one mole is this many particles, by definition
- k_B = 1.380649 × 10⁻²³ J K⁻¹ Boltzmann constant · defines the kelvin — it turns a temperature into an energy per particle
How much room one mole of any ideal gas takes up
| Condition | Temperature | Pressure | Molar volume |
|---|---|---|---|
| IUPAC standard (0 °C, 100 kPa) | 273.15 K | 100 kPa | 22.711 L/mol |
| 0 °C at one atmosphere | 273.15 K | 101.325 kPa | 22.414 L/mol |
| Room temperature (25 °C) | 298.15 K | 101.325 kPa | 24.465 L/mol |
| Boiling water (100 °C) | 373.15 K | 101.325 kPa | 30.620 L/mol |
Computed live as V/n = R·T/p, using the exact molar gas constant from our constants page. The answer does not depend on which gas it is — that is what makes it ideal.
R stopped being a measured number in 2019
The 2019 SI redefinition fixed the Boltzmann constant (which defines the kelvin) and the Avogadro constant (which defines the mole). The gas constant is their product, R = N_A · k_B, so it inherited their exactness — 8.314 462 618… J mol⁻¹ K⁻¹, with no uncertainty left to measure.
See the seven defining constants →