Combined gas law calculator
A gas moving between two states: p₁V₁/T₁ = p₂V₂/T₂.
Fill in the fields and the result will appear here automatically.
Compares two states of the same amount of ideal gas and finds the second state’s pressure, volume or temperature. The amount must remain fixed: leakage, added gas or a change in the gas phase breaks this assumption. Pressure is absolute in kPa, volume is in litres and temperature is in kelvin. The relation describes states, not the rate of heating or compression.
How it works
Formula and logic
For fixed n, pV = nRT gives p₁V₁/T₁ = p₂V₂/T₂. Thus p₂ = p₁(V₁/V₂)(T₂/T₁), V₂ = V₁(p₁/p₂)(T₂/T₁), and T₂ = T₁(p₂/p₁)(V₂/V₁). All known p, V and T must be positive. The two displayed pV/T values agree up to rounding. Both states use the same pressure and volume units; 1 kPa·L = 1 J.
Example
100 kPa, 2 L and 300 K compressed to 1 L at 300 K give p₂ = 200 kPa; pV/T is 2/3 kPa·L/K in both states. At constant 100 kPa, heating from 300 to 600 K expands 2 L to 4 L.
Fields and units
- What to find — list option
- Pressure p₁ — kPa
- Volume V₁ — L
- Temperature T₁ — K
- Pressure p₂ — kPa
- Volume V₂ — L
- Temperature T₂ — K
How to use
- — Choose the unknown second-state quantity: p₂, V₂ or T₂.
- — Enter positive absolute p₁ in kPa, V₁ in litres and T₁ in K.
- — Fill in the two visible known second-state quantities; read the unknown in the result.
- — Convert Celsius manually before entering temperature: T = t + 273.15. These fields accept K.
- — If a gauge reports pressure relative to the surroundings, first add the actual ambient pressure in the same unit to obtain absolute pressure.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax Chemistry 2e §9.2: ideal and combined gas laws, units and model limits
- Limitation
- Combined law for a fixed amount of ideal gas and positive absolute p, V and T. Substance-specific properties, phase changes and non-ideal corrections are not calculated. Agreement of pV/T checks the model’s algebra, not its accuracy for a real gas.
FAQ
How does the combined gas law differ from PV = nRT?
It connects two states with the same amount of substance, so nR cancels. A single state or a changed amount requires the equation with moles.
Why cannot the combined law use ratios of Celsius temperatures?
Only absolute temperature has the required ratio scale. 10 → 20 °C is 283.15 → 293.15 K, an increase of about 3.53%, not a doubling.
Which individual laws follow when a quantity stays fixed?
At fixed T, pV is constant (Boyle); at fixed p, V/T is constant (Charles); at fixed V, p/T is constant. The amount of gas must remain fixed in every case.
Can I compare states after some gas has leaked?
No. Then n changes and the equality of the two pV/T values no longer follows. Use the amount of substance in each state and the full equation.
Can a gauge reading be entered as p₁ or p₂?
Only when it is an absolute-pressure reading. For gauge pressure, p_abs = p_gauge + p_ambient; ambient pressure need not be 100 kPa or one standard atmosphere.
When is the combined law only an approximation?
Real gases tend towards ideal behaviour at relatively low pressure and away from condensation. There is no pressure threshold valid for every substance; this form does not model phase changes or changing gas amount.