Engineering
Ideal Gas Law (PV = nRT) and Combined Gas Law formulas
Solve pressure, volume, or moles with PV = nRT and scale compressed-gas states via (P1*V1)/T1 = (P2*V2)/T2 using mandatory Kelvin temperatures.
Always convert Celsius to absolute Kelvin (+ 273.15) inside gas laws!
The Ideal Gas Law P * V = n * R * T_K relates Pressure P, Volume V, Moles n, Gas Constant R (0.082057 L*atm/(mol*K) or 8.31446 J/(mol*K)), and Absolute Temperature T_K = TempC + 273.15. Using raw Celsius (0°C or -10°C) produces zero or negative pressures!
For a sealed cylinder changing volume and temperature (Combined Gas Law encompassing Boyle's, Charles's, and Gay-Lussac's laws), n*R cancels out: P2 = P1 * (V1 / V2) * ((T2_C + 273.15) / (T1_C + 273.15))!
| Gas Engineering Equation | Inputs | Calculated Output |
|---|---|---|
| Ideal Gas Pressure P = nRT / V | 2 mol, 25°C (298.15 K), 10 L | 4.8931 atm |
| Boyle's Compression (Halve V, same T) | P1 = 2 atm, V1 = 12L -> V2 = 6L | 4.00 atm (2x P) |
| Combined Compression + Heating | 12L->6L & 300K->450K | 6.00 atm (2 * 1.5x P) |
Ideal Gas Law pressure (atm) and Combined Gas Law state formulas
Uses R = 0.082057 L*atm/(mol*K) when Volume is in Liters and Pressure in Atmospheres.
=ROUND((A2 * 0.082057 * (B2 + 273.15)) / C2, 4)Combined Gas Law final pressure P2 from (P1, V1, T1_C -> V2, T2_C)
Converts both initial and final Celsius temperatures to Kelvin (+ 273.15) automatically.
=ROUND(D2 * (E2 / G2) * ((H2 + 273.15) / (F2 + 273.15)), 4)Inputs and interpretation
Use absolute pressure, positive absolute temperatures and volumes, and a fixed amount of gas for the combined law. Match pressure/volume units to R; gauge pressure is not absolute pressure. This ideal-gas approximation can fail at high density or near condensation. These equations do not establish safe cylinder operating limits.
Try the example
Use the original values or change them to test your understanding.