Combined Gas Law Calculator
Enter the initial and final pressure, temperature, and initial volume; by the combined gas law P₁V₁/T₁ = P₂V₂/T₂ it instantly computes the gas volume in the new state for a fixed amount of gas.
Input Data
Results
At a glance:Enter the initial and final pressure, temperature, and initial volume; by the combined gas law P₁V₁/T₁ = P₂V₂/T₂ it instantly computes the gas volume in the new state for a fixed amount of gas.
Formula
P₁V₁/T₁ = P₂V₂/T₂.
Final volume V₂ = P₁·V₁·T₂ / (T₁·P₂).
$$\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$$$$V_2 = \dfrac{P_1 V_1 T_2}{T_1 P_2}$$How to Use
- Enter the initial P₁, V₁, T₁ and final P₂, T₂ (in K).
- The calculator returns the final volume V₂.
Effect of simultaneous pressure and temperature changes on gas volume (initial 1 atm, 2 L, 273 K)
| Final pressure P₂ | Final temperature T₂ | Final volume V₂ | Note |
|---|---|---|---|
| 1 atm | 273 K | 2 L | No change |
| 2 atm | 273 K | 1 L | Compression only (Boyle) |
| 1 atm | 546 K | 4 L | Heating only (Charles) |
| 2 atm | 546 K | 2 L | Compression + heating cancel out |
| 0.5 atm | 546 K | 8 L | Decompression + heating both expand |
V₂ = P₁·V₁·T₂/(T₁·P₂); temperature in absolute scale K.
FAQ
Why must temperature be in kelvin?
Because in gas laws temperature reflects average molecular kinetic energy, which is proportional to absolute temperature, starting from absolute zero (0 K = −273.15°C). Using Celsius would treat 0°C as zero kinetic energy and make negative temperatures break the ratio. Always use K = °C + 273.15.
Relation between the combined gas law and Boyle's/Charles's laws?
The combined gas law P₁V₁/T₁ = P₂V₂/T₂ integrates all three. At constant temperature it reduces to Boyle's law P₁V₁ = P₂V₂; at constant pressure to Charles's law V₁/T₁ = V₂/T₂; at constant volume to Gay-Lussac's law P₁/T₁ = P₂/T₂.
Must the pressure units match?
Yes. Both sides of the equation must use the same pressure unit (atm or kPa) and the same volume unit. Because it is a ratio, the unit kind does not affect the result, but both sides must be the same kind and unit; temperature is always kelvin.
How is it different from the ideal gas equation PV = nRT?
The combined gas law applies to comparing two states with 'unchanged gas amount, only P, V, T changing', without needing moles n. The ideal gas equation PV = nRT also handles cases where the gas amount changes and gives absolute values directly. The former is a corollary of the latter when n is fixed.
What if gas leaks or is added?
The combined gas law assumes constant moles. If gas leaks, is added, or reacts to change the amount, you cannot directly use P₁V₁/T₁ = P₂V₂/T₂; switch to the ideal gas equation PV = nRT and substitute each state's n separately.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.