Ideal Gas Law Calculator
Moles (n)
1
How it works
The ideal gas law relates pressure (P), volume (V), number of moles (n), and temperature (T): PV = nRT, where R = 8.314 J/(mol·K). Alternatively, PV = NkT where N is number of molecules and k is Boltzmann's constant. The ideal gas approximation holds well at low pressures and high temperatures — real gases deviate at high pressure or near condensation.
**Combined gas law** When the amount of gas is constant: P₁V₁/T₁ = P₂V₂/T₂. This allows calculation of new state after a change. A gas at 1 atm, 1 L, 300 K compressed to 0.5 L and 400 K: P₂ = P₁ × V₁/V₂ × T₂/T₁ = 1 × 2 × (400/300) = 2.67 atm.
**Ideal gas assumptions and their limits** The model assumes: molecules occupy no volume (negligible compared to container), no intermolecular forces, elastic collisions only. Real gases deviate especially near phase boundaries. van der Waals equation: (P + a/V²)(V - b) = nRT corrects for intermolecular attractions (a) and finite molecular volume (b).
**Applications** Internal combustion engines: compressing the air-fuel mixture raises temperature (compression ratio effect) — the ideal gas law predicts this temperature rise. Pneumatic systems: calculate pressure in a tank as temperature changes or gas is added. Altitude and weather: the atmosphere approximates ideal gas behavior — understanding pressure, temperature, and density relationships is fundamental to aviation and meteorology.
**Absolute temperature and pressure** The ideal gas law requires absolute temperature (Kelvin = Celsius + 273.15) and absolute pressure (gauge pressure + atmospheric pressure). Common errors: using Celsius instead of Kelvin, or gauge PSI instead of absolute PSI (PSIA).
Frequently Asked Questions
- PV = nRT. For a standard 40-liter oxygen cylinder at 150 bar (15 MPa): n = PV/RT = (15,000,000 × 0.040) / (8.314 × 293) = 246 moles. At 1 bar and 20°C, this occupies V = nRT/P = 246 × 8.314 × 293 / 100,000 = 6.0 m³ = 6,000 liters. As gas is used, pressure drops proportionally. Note: real high-pressure gases deviate from ideal — oxygen at 150 bar is approximately 6% denser than ideal. The Van der Waals equation is more accurate for high-pressure calculations.
- PV/T = constant for fixed amount of gas. If temperature drops from 20°C (293 K) to -10°C (263 K) at constant volume: P_cold = P_warm × 263/293 = 0.897 × P_warm. A tire at 32 PSI drops to 28.7 PSI — 3.3 PSI drop per 30°C temperature change. US industry rule of thumb: 1 PSI per 10°F (~0.7 PSI per 5°C). Underinflated tires run hotter (more flexing), wear unevenly, reduce fuel economy, and can fail suddenly. Check tire pressure when cold (not after driving) for accurate readings.
- Atmospheric pressure decreases with altitude: at 10,000 m (33,000 ft, typical cruise altitude), pressure is ~26 kPa (0.26 atm). Without pressurization, PO₂ is insufficient for consciousness (hypoxia occurs above ~3,000 m without acclimatization). Aircraft cabins are pressurized to equivalent altitudes of 1,500–2,400 m (6,000–8,000 ft). The fuselage must withstand the differential pressure (cabin pressure minus outside pressure) — structural fatigue from pressurization cycles is the primary limiting factor in aircraft design life.
- Absolute pressure = gauge pressure + atmospheric pressure (101.325 kPa = 14.696 PSI at sea level). A tire inflated to '32 PSI' is 32 PSI gauge pressure (PSIG) = 32 + 14.7 = 46.7 PSI absolute (PSIA). Vacuum pressure: negative gauge pressure — a 50 kPa vacuum is 50 kPa below atmospheric = 51.3 kPa absolute. The ideal gas law requires absolute pressure and absolute temperature (Kelvin). A common error: using gauge pressure in PV=nRT gives wrong answers. Always convert gauge to absolute before substituting into any thermodynamic equation.