Boyle's Law Calculator
Enter initial pressure, initial volume and final pressure to instantly compute the final gas volume under Boyle's law P₁V₁ = P₂V₂ at constant temperature.
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Results
At a glance:Boyle's law is one of the three empirical gas laws, proposed by the Irish-born chemist Robert Boyle in 1662. It states that for a fixed amount of gas (constant moles) at constant temperature (isothermal), pressure P and volume V are inversely proportional — higher pressure gives smaller volume and vice versa, with their product constant. In formula, P·V = constant, so comparing two states of the same gas gives P₁·V₁ = P₂·V₂ (subscript 1 = initial, 2 = final). To find the changed volume, rearrange to V₂ = P₁·V₁ / P₂. Microscopically: gas pressure comes from molecules hitting the container wall; at constant temperature (unchanged average molecular speed), compressing the gas into a smaller volume makes molecules denser and hit the wall more often, raising pressure; expansion lowers it. In the default example: a gas at 1 atm occupies 10 L; compress it to 2.5 atm and the volume becomes V₂ = 1×10/2.5 = 4 L; check P₁V₁ = 1×10 = 10, P₂V₂ = 2.5×4 = 10, equal products, law satisfied. Applications: (1) syringes, pistons, barometers — block the syringe outlet and push the plunger, volume drops and pressure rises; (2) respiratory physiology — inhaling expands the chest and lung volume, dropping intrapulmonary pressure below atmospheric so air is 'sucked' in; (3) diving safety — ascending divers face falling water pressure and lung gas expands per Boyle's law; holding breath while ascending can over-expand the lungs, so continuous exhalation is required; (4) industrial gas compression/storage and pneumatic design. Caveats: temperature must stay constant (it is an isothermal law; if temperature changes use the combined gas law P₁V₁/T₁ = P₂V₂/T₂); the amount of gas (moles) must stay constant; pressure units must match on both sides (all atm, or all kPa/mmHg), as must volume units; Boyle's law describes ideal gases and real gases deviate near liquefaction at low temperature/high pressure, though most gases approximate it at room conditions. Together with Charles's law (V∝T at constant P) and Gay-Lussac's law (P∝T at constant V), it forms the three gas laws unified by the ideal gas equation PV = nRT. This calculator quickly finds the isothermal final volume from initial pressure, initial volume and final pressure.
Formula
Boyle's law (isothermal): P₁ · V₁ = P₂ · V₂ (PV = constant).
Final volume: V₂ = P₁ · V₁ ÷ P₂.
Final pressure (reverse): P₂ = P₁ · V₁ ÷ V₂.
Premises: constant temperature, constant amount of gas.
$$P_1 V_1 = P_2 V_2$$$$V_2 = \dfrac{P_1 V_1}{P_2}$$How to Use
- Enter the initial gas pressure P₁ and initial volume V₁.
- Enter the final pressure P₂ after the change (same unit as P₁).
- The right panel instantly shows the isothermal final volume V₂.
Effect of pressure change on gas volume at constant temperature (initial 1 atm, 10 L)
| Final Pressure P₂ | Pressure Multiple | Final Volume V₂ | P₂·V₂ Check |
|---|---|---|---|
| 0.5 atm | 0.5× | 20 L | 10 |
| 1 atm | 1× | 10 L | 10 |
| 2 atm | 2× | 5 L | 10 |
| 2.5 atm | 2.5× | 4 L | 10 |
| 5 atm | 5× | 2 L | 10 |
V₂ = P₁·V₁/P₂; doubling pressure halves volume, product P·V stays 10 (conserved).
Case Studies
Compressing gas to 2.5 atm
A gas initially at 1 atm occupies 10 L; compress it isothermally to 2.5 atm.
Final volume V₂ = P₁·V₁/P₂ = 1 × 10 / 2.5 = 4 L.
Check P₁V₁ = 10, P₂V₂ = 2.5×4 = 10, products equal, consistent with Boyle's law.
Bubble expansion as a diver ascends
A diver at 10 m depth (about 2 atm) exhales a 0.5 L bubble that rises to the surface (1 atm).
Assuming constant temperature, bubble volume V₂ = 2 × 0.5 / 1 = 1 L, doubling.
This shows lung gas expands during ascent; continuous exhalation is required to avoid lung over-expansion injury.
FAQ
What are the premises of Boyle's law?
Two key premises: temperature stays constant (isothermal) and the amount of gas (moles) stays constant. Only then are pressure and volume strictly inversely proportional, P₁V₁=P₂V₂. If temperature changes, use the combined gas law P₁V₁/T₁=P₂V₂/T₂.
Must pressure be in atm?
Not necessarily. Because Boyle's law is a ratio, pressure can be atm, kPa, mmHg or bar — as long as initial and final pressures use the same unit; volume likewise. The unit type does not affect the numeric result of V₂.
Why does larger pressure give smaller volume?
Gas pressure comes from molecules hitting the container wall. At constant temperature the molecular speed is unchanged; compressing the gas into a smaller volume makes molecules denser and hit the wall more often, raising pressure. Thus at fixed temperature and amount, pressure and volume must trade off.
How is Boyle's law related to the ideal gas equation?
In the ideal gas equation PV = nRT, if n (amount) and T (temperature) are fixed, then PV = constant — exactly Boyle's law. Boyle's law is the special case of the ideal gas equation under isothermal, fixed-amount conditions.
Do real gases obey Boyle's law?
Most gases approximate it at room temperature and pressure. But at low temperature and high pressure (near liquefaction), intermolecular forces and molecular volume become significant and real gases deviate, requiring corrections such as the van der Waals equation.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.