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** determines gas temperature from pressure, volume, and moles using T = PV/(nR). Temperature is perhaps the most fundamental thermodynamic property — it determines the average kinetic energy of molecules and drives all heat transfer processes.
Gas thermometry is actually one of the most accurate methods for measuring temperature. Because the ideal gas law is universal, measuring the pressure of a known quantity of gas in a known volume directly gives temperature without calibration against arbitrary standards. This principle underpins the definition of the Kelvin scale itself.
Enter pressure, volume, and moles to find the temperature in Kelvin, Celsius, Fahrenheit, and Rankine, along with molecular kinetic energy and RMS molecular speed. Reference tables show how volume varies with temperature at your specified pressure. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results.
Whether solving thermodynamics problems, interpreting experimental data, or designing gas-based temperature sensors, this calculator provides instant temperature determination from measurable gas properties with comprehensive unit support. Keep these notes focused on your current workflow. Tie the context to real calculations your team runs. Use this clarification to avoid ambiguous interpretation. Align the note with how outputs are reviewed.
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.
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.