Boyle's Law Calculator
Apply Boyle's law, P₁V₁ = P₂V₂, to find the new pressure or volume of a fixed amount of gas at constant temperature when the other changes.
كيفية استخدام هذه الحاسبة
- 1Choose whether you're solving for the final volume or the final pressure.
- 2Enter the initial pressure and volume.
- 3Enter the known final pressure or volume.
- 4Read the result — pressure and volume always trade off inversely.
طريقة الحساب
Boyle's law
P₁ V₁ = P₂ V₂ V₂ = P₁V₁ ÷ P₂, P₂ = P₁V₁ ÷ V₂ pressure × volume = constant (at fixed temperature) pressure and volume are inversely proportional
Boyle's law describes how the pressure and volume of a fixed quantity of gas relate when the temperature is held constant. It states that pressure and volume are inversely proportional: as one increases, the other decreases in exact proportion, so their product remains constant. Compress a gas into half its volume and its pressure doubles; let it expand to twice the volume and its pressure halves. This is captured in the equation P₁V₁ = P₂V₂, which says the pressure-times-volume before a change equals the pressure-times-volume after. Given any three of the four quantities, the fourth follows by rearrangement. Because the same units appear on both sides of the equation, they cancel, so any consistent units of pressure and volume can be used. The law is a special case of the ideal gas law with temperature and amount of gas fixed, and it holds well for real gases except at very high pressures.
مثال محلول
A gas occupying 10 litres at a pressure of 1 atmosphere, compressed at constant temperature until its pressure reaches 2 atmospheres, shrinks to V₂ = (1 × 10) ÷ 2 = 5 litres — exactly half the volume for double the pressure, as the inverse relationship demands.
Boyle's Law Calculator: الدليل الكامل
The inverse dance of pressure and volume
Boyle's law, discovered by Robert Boyle in the 17th century, was one of the first quantitative gas laws and remains a cornerstone of understanding how gases behave. Its content is simple but not obvious: for a trapped quantity of gas at a steady temperature, squeezing it into a smaller space raises its pressure, and letting it expand lowers its pressure, in exact inverse proportion. Halve the volume and the pressure doubles; third the volume and the pressure triples. The product of pressure and volume is a fixed number that the gas holds onto as it is compressed or expanded.
The molecular picture makes this intuitive. A gas exerts pressure because its molecules constantly collide with the walls of their container. Squeeze the gas into half the space and the molecules, now packed twice as densely, strike the walls twice as often, doubling the pressure. Expand the gas and the collisions become less frequent, lowering the pressure. Temperature must be held constant for this clean relationship, because heating the gas would speed the molecules and change the pressure independently. Under that condition, the inverse relationship is precise, and it is what Boyle's law expresses.
Boyle's law in the body and the world
Boyle's law is not a laboratory curiosity; it governs breathing itself. When you inhale, your diaphragm contracts and your chest expands, increasing the volume of your lungs. By Boyle's law, that larger volume means lower pressure inside the lungs than in the atmosphere, so air rushes in to equalise. Exhaling reverses it: the chest shrinks, lung volume falls, internal pressure rises above atmospheric, and air flows out. Every breath you take is Boyle's law in action, driven by muscles changing the volume of a gas-filled space.
The same principle appears wherever gases are compressed or expanded. A syringe draws in fluid because pulling the plunger increases the volume and drops the pressure. Bicycle pumps, pneumatic tools, and gas storage all rely on the pressure-volume trade-off. It is especially critical in scuba diving, where the surrounding water pressure changes dramatically with depth: a lungful of air at depth expands as a diver ascends and the pressure drops, which is why divers are trained never to hold their breath while ascending — the expanding gas could rupture the lungs. Boyle's law turns the abstract relationship between pressure and volume into a matter of real physical and even medical consequence.
The limits: temperature and real gases
Boyle's law comes with two important conditions, and understanding them prevents misuse. The first is constant temperature. The clean inverse relationship holds only when the gas is neither heated nor cooled during the change. In practice, compressing a gas tends to warm it and expanding it tends to cool it — anyone who has felt a bicycle pump grow hot has experienced this. To apply Boyle's law strictly, the process must be slow enough, or the container conductive enough, for the temperature to stay constant. When temperature does change, the fuller ideal gas law, which includes temperature, is needed instead.
The second condition is that the gas behaves ideally, meaning its molecules are treated as taking up no space and exerting no forces on each other except during collisions. This is an excellent approximation for real gases at ordinary pressures, which is why Boyle's law works so well in everyday situations. But at very high pressures, where molecules are forced close together, the finite size of the molecules and the attractions between them become significant, and real gases deviate from the law. For most practical purposes these deviations are negligible, but they remind us that Boyle's law is an idealisation — a superb one within its range, and part of the larger framework of the ideal gas law that generalises it.
الأسئلة الشائعة
What is Boyle's law?
Boyle's law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Squeeze a gas into half the volume and its pressure doubles. Their product stays constant as the gas is compressed or expanded.
How do I use the P1V1 = P2V2 formula?
Identify the three values you know and solve for the fourth. To find the new volume, V₂ = P₁V₁ ÷ P₂. A gas at 1 atm and 10 L compressed to 2 atm becomes (1 × 10) ÷ 2 = 5 L. Any consistent units work, since they cancel.
Why are pressure and volume inversely related?
Because pressure comes from gas molecules hitting the container walls. Compress the gas into a smaller volume and the molecules, now denser, strike the walls more often, raising the pressure. Halving the volume doubles the collision rate and so doubles the pressure, at constant temperature.
When does Boyle's law not apply?
When the temperature changes — compressing a gas tends to warm it, which needs the fuller ideal gas law — or at very high pressures, where real gases deviate because molecular size and attractions matter. For a fixed amount of gas at constant temperature and ordinary pressures, it holds very well.