Calculate gas temperature using T = PV/(nR). Find temperature from pressure, volume, and moles with all temperature scales and molecular kinetics.
The **Ideal Gas Temperature Calculator** solves T = PV/(nR) to find gas temperature from pressure, volume, and moles. It reports the result in Kelvin, Celsius, Fahrenheit, and Rankine so you can move between scientific and everyday temperature scales without redoing the algebra.
In the ideal-gas model, temperature is the quantity that ties pressure and volume together. That is why gas thermometry has long been used as a reference method: if you know the gas amount, the container volume, and the pressure, you can infer temperature directly.
The page also shows molecular kinetic context and a volume-vs-temperature reference table so the answer is easier to interpret in thermodynamic terms.
Temperature is often the missing variable in gas-law problems, and solving for it by hand is easy to mix up with the pressure or volume forms of the equation. Putting the algebra, unit conversions, and kinetic interpretation together helps you confirm whether a measured gas state makes physical sense.
T = PV / (nR) Where: T = temperature (K), P = pressure (Pa), V = volume (m³), n = moles, R = 8.31446 J/(mol·K)
Result: 273.15 K (0.00°C)
T = (101325 Pa)(0.022414 m³) / (1 mol × 8.31446) = 273.15 K = 0°C. This confirms STP conditions — 1 mole at 1 atm in 22.414 L is exactly 0°C.
Temperature fundamentally measures molecular motion. In an ideal gas, the average kinetic energy per molecule is exactly (3/2)k_BT, where k_B = 1.381 × 10⁻²³ J/K is Boltzmann's constant. This remarkable result means temperature has a direct microscopic interpretation — it is proportional to how fast molecules move.
At room temperature (300 K), nitrogen molecules in air have an average speed of about 515 m/s, while hydrogen molecules move at nearly 1,900 m/s (lighter molecules move faster at the same temperature). This explains why hydrogen escapes from Earth's atmosphere more readily than nitrogen.
**Primary Temperature Standards:** Constant-volume gas thermometers are used to define temperature scales. The triple point of water (273.16 K) provides the calibration point, and pressure measurements at other temperatures give accurate thermodynamic temperatures.
**Extreme Temperature Measurement:** Gas thermometry works from about 3 K to 1,300 K. Below 3 K, other methods (nuclear magnetic resonance, noise thermometry) are needed. Above 1,300 K, radiation pyrometry takes over.
**Research Applications:** Ultra-cold gas experiments studying Bose-Einstein condensation, superfluidity, and quantum phase transitions require temperature measurements at nanokelvin levels — far beyond the reach of gas thermometry but building on the same fundamental concepts.
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No — 0 K (absolute zero) is the lowest possible temperature, where molecular motion ceases. The ideal gas law gives T = 0 only when PV = 0, which means either no pressure, no volume, or no gas.
Temperature measures the average translational kinetic energy per molecule: E_avg = (3/2)k_BT. Higher temperature means faster-moving molecules.
Kelvin is the absolute (thermodynamic) scale. Celsius is offset by 273.15 from Kelvin. Fahrenheit uses a different zero point and degree size. Rankine is the absolute version of Fahrenheit.
Constant-volume gas thermometry with helium can achieve uncertainties below 0.001 K. It is one of the primary methods for realizing the ITS-90 temperature scale.
Root-mean-square speed is √(3RT/M), representing the effective speed of gas molecules. At room temperature, air molecules move at about 500 m/s — faster than the speed of sound.
Near absolute zero, quantum effects dominate and the ideal gas law breaks down. Real gases liquefy or solidify well above 0 K. Helium remains gaseous the longest, liquefying at 4.2 K.