OneTaskBy Tim King · Updated
Combined Gas Law Calculator
Solve for Any Missing Value in Boyle's, Charles's and Gay-Lussac's Laws
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How the Combined Gas Law Calculator works
This combined gas law calculator finds the missing value when a fixed amount of gas changes pressure, volume or temperature. Fill in five of the six boxes and leave the one you want empty. It handles Boyle's, Charles's and Gay-Lussac's laws as special cases, and converts °C or °F to kelvin for you.
When a sealed amount of gas is squeezed, heated or cooled, its pressure, volume and absolute temperature move together in a fixed way. The combined gas law ties all three into one equation, so you can predict what a tyre, a syringe or a weather balloon will do when conditions change.
How the combined gas law calculator works
The formula is P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂, with temperatures in kelvin. Hold temperature constant and it becomes Boyle's law, P₁V₁ = P₂V₂. Hold pressure constant and it is Charles's law, V₁ ÷ T₁ = V₂ ÷ T₂. Hold volume constant and it is Gay-Lussac's law, P₁ ÷ T₁ = P₂ ÷ T₂. To keep a property constant, enter the same value in both boxes.
First example. 2 L of air at 101.325 kPa and 20 °C is compressed to 200 kPa and warms to 50 °C. V₂ = 101.325 × 2 × 323.15 ÷ (293.15 × 200) = 1.117 L.
Second example. A tyre at 220 kPa absolute and 15 °C heats to 45 °C on a long drive. At fixed volume, P₂ = 220 × 318.15 ÷ 288.15 = 242.9 kPa, a 10.4% rise.
How many litres will 1 L of gas fill if heated from 20 °C to 100 °C? At constant pressure, 1 × 373.15 ÷ 293.15 = 1.27 L.
A 1 L sample at 20 °C and 101.325 kPa under new conditions
| Temperature (°C) | Volume at constant pressure (L) | Pressure in a sealed 1 L container (kPa) | Change from 20 °C |
|---|---|---|---|
| -40 | 0.795 | 80.6 | -20.5% |
| -30 | 0.829 | 84.0 | -17.1% |
| -20 | 0.864 | 87.5 | -13.6% |
| -10 | 0.898 | 91.0 | -10.2% |
| 0 | 0.932 | 94.4 | -6.8% |
| 10 | 0.966 | 97.9 | -3.4% |
| 20 | 1.000 | 101.3 | +0.0% |
| 30 | 1.034 | 104.8 | +3.4% |
| 40 | 1.068 | 108.2 | +6.8% |
| 50 | 1.102 | 111.7 | +10.2% |
| 60 | 1.136 | 115.2 | +13.6% |
| 70 | 1.171 | 118.6 | +17.1% |
| 80 | 1.205 | 122.1 | +20.5% |
| 90 | 1.239 | 125.5 | +23.9% |
| 100 | 1.273 | 129.0 | +27.3% |
| 110 | 1.307 | 132.4 | +30.7% |
| 120 | 1.341 | 135.9 | +34.1% |
| 130 | 1.375 | 139.3 | +37.5% |
| 140 | 1.409 | 142.8 | +40.9% |
| 150 | 1.443 | 146.3 | +44.3% |
| 160 | 1.478 | 149.7 | +47.8% |
| 170 | 1.512 | 153.2 | +51.2% |
| 180 | 1.546 | 156.6 | +54.6% |
| 190 | 1.580 | 160.1 | +58.0% |
| 200 | 1.614 | 163.5 | +61.4% |
Tips and pitfalls
- Kelvin only. Going from 10 °C to 20 °C does not double the volume; the calculator converts every temperature to kelvin before solving.
- Absolute pressure. Gauge readings must have atmospheric pressure added first, or the ratios come out wrong.
- Same units both sides. P₁ and P₂ share one unit, as do V₁ and V₂, so no conversion is needed between them.
- Fixed amount of gas. If gas leaks in or out, use the ideal gas law with moles instead.
FAQ
What is the combined gas law?
The combined gas law states that P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ for a fixed amount of gas. It merges Boyle's, Charles's and Gay-Lussac's laws into one equation, so you can handle a change in pressure, volume and temperature at the same time.
How do I use it for Boyle's law?
Enter the same temperature for T₁ and T₂, then fill in three of the pressures and volumes. The temperatures cancel, leaving P₁V₁ = P₂V₂. Halving the volume of a gas at constant temperature doubles its pressure, which is how a bicycle pump works.
How do I use it for Charles's law?
Enter the same pressure for P₁ and P₂. The equation then becomes V₁ ÷ T₁ = V₂ ÷ T₂, so volume grows in proportion to absolute temperature. A balloon taken from a 20 °C room into a −10 °C garden shrinks by about 10%.
Why must temperatures be in kelvin?
Gas laws depend on absolute temperature measured from absolute zero. Celsius and Fahrenheit put zero at arbitrary points, so ratios between them are meaningless. The calculator accepts °C, K or °F and converts to kelvin internally before solving.
What is the difference between the combined and ideal gas laws?
The combined gas law compares one fixed sample of gas in two states and needs no gas constant. The ideal gas law, PV = nRT, describes a single state and brings in the number of moles, so it can find how much gas is present.
See also: all Chemistry tools, Physics, Electronics.
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