Class 9 > Unit # 07:Properties of Matter > Boyle's Law

Talha's Physics Academy

Boyle's Law: Statement, Derivation & Graphs

State and Explain Boyle’s Law. Also draw its graphs.

Statement

"The volume of a fixed mass of a gas is inversely proportional to its pressure, provided its temperature remains constant."

Mathematical Derivation

If $P$ represents the pressure exerted on the surface of the gas and $V$ represents the volume of the gas, then mathematically at constant temperature:

$V \propto \frac{1}{P} \quad \text{or} \quad V = \frac{k}{P} \quad \Rightarrow \quad PV = k \quad (\text{constant})$

Let $P_1$ and $V_1$ represent the initial pressure and initial volume of a gas. If at a constant temperature we increase the pressure from $P_1$ to $P_2$, its volume will decrease from $V_1$ to $V_2$:

• At initial state: $P_1 V_1 = k$     --- (i)
• At final state: $P_2 V_2 = k$     --- (ii)

Equating equations (i) and (ii), since the constant $k$ remains unchanged for a fixed mass of gas at constant temperature:

$$P_1 V_1 = P_2 V_2$$

Fig: Effect of increasing pressure on gas volume in a cylinder piston model ($P_2 > P_1$, $V_2 < V_1$).

Graphical Representation

The relationship described by Boyle's law can be represented graphically in two standard ways:

• (a) $P\text{-}V$ Graph: The curve between pressure ($P$) and volume ($V$) shows that if pressure increases, volume decreases and vice versa (forming a rectangular hyperbola).
• (b) $P\text{-}\frac{1}{V}$ Graph: The graph plotted between pressure ($P$) and inverse volume ($\frac{1}{V}$) yields a straight line passing through the origin, confirming direct proportionality between $P$ and $\frac{1}{V}$.

Fig: Graphical representation of Boyle's Law showing (a) inverse curved relationship and (b) linear direct proportionality with inverse volume.

© 2026 Talha's Physics Academy. All rights reserved.