Boyle's Law: Pressure-Volume Relationship

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Boyle's Law

The Pressure-Volume Relationship at Constant Temperature.

By chemca Team • Updated Aug 2026

In 1662, Anglo-Irish chemist Robert Boyle performed a series of experiments using a J-shaped glass tube to trap air with mercury. He discovered the first, and perhaps most fundamental, of the gas laws: the inverse relationship between the pressure and volume of a gas.

1. Statement & Mathematical Formula

Boyle's Law states: At a constant temperature, the volume of a fixed mass of a dry gas is inversely proportional to its pressure.

If you squeeze a gas into half its original volume, the molecules hit the walls twice as often, doubling the pressure.

$$V \propto \frac{1}{P} \quad (\text{at constant } T \text{ and } n)$$
$$PV = k \quad (\text{where } k \text{ is a constant})$$

The Problem-Solving Equation:

If a gas undergoes a change in conditions from state 1 to state 2 at constant temperature, we use:

$$P_1V_1 = P_2V_2$$

2. Graphical Representation (Isotherms)

Graphs drawn at a constant temperature are called Isotherms (iso = same, therm = heat/temperature). Identifying these graphs is a highly favored question format in competitive exams.

P vs V
(Rectangular Hyperbola)
T₂ > T₁

P vs 1/V
(Straight Line through Origin)
T₂ > T₁

PV vs P
(Horizontal Line parallel to X-axis)
T₂ > T₁

Higher Temperatures = Higher Curves: Notice that in all the graphs, the curve/line corresponding to a higher temperature ($T_2$) lies above or further from the axes compared to the lower temperature ($T_1$). This is because at higher temperatures, for a given pressure, the volume is greater (Charles's Law).

3. Boyle's Law & Density

Because gases compress under pressure, their density changes. We know that Density ($d$) is Mass ($m$) divided by Volume ($V$).

$$d = \frac{m}{V} \implies V = \frac{m}{d}$$

Substituting $V$ into Boyle's Equation ($P \times V = k$):

$$P \times \left(\frac{m}{d}\right) = k \implies \frac{P}{d} = \frac{k}{m} = k' \text{ (constant)}$$

Conclusion: At constant temperature, the density of a fixed mass of gas is directly proportional to its pressure ($P \propto d$).

4. Real-Life Applications

• Breathing (Respiration): When your diaphragm drops, the volume of your lungs increases. According to Boyle's law, the pressure inside drops below atmospheric pressure, causing air to rush in.
• Scuba Diving: As a diver ascends to the surface, the water pressure decreases. Consequently, the volume of the air bubbles they exhale expands significantly as they rise. (This is also why ascending too quickly can cause lung barotrauma).
• Syringes: Pulling the plunger back increases the volume inside the barrel, dropping the pressure. Fluid is then pushed into the syringe by the higher atmospheric pressure outside.

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