Boyle’s Law

Boyle’s Law is one of the fundamental gas laws in physics and chemistry that explains how gases behave under pressure. Proposed by Robert Boyle in 1662, it reveals a beautiful connection between pressure and volume of a gas when the temperature remains constant. 

This article is on Boyle’s Law simply and practically, along with its formula, derivation, and everyday applications. 

Table of Contents 

• What is Boyle’s Law?
• Graphical Representation of Boyle’s Law
• Real-Life Examples of Boyle’s Law
• Solved Example Problems

What is Boyle’s Law?

Boyle’s Law states that the pressure of a gas is inversely proportional to its volume, provided the temperature and the amount of gas remain constant.

 

In simple terms, when the volume of a gas decreases, its pressure increases and vice versa.

Mathematically, this can be written as:

P1∝1V1

When a constant of proportionality (k) is introduced, it becomes:

P=k×1V⇒P×V=k

Here,

• P = Pressure of the gas

• V = Volume of the gas

• k = Constant for a given mass of gas at constant temperature

This means that for a fixed amount of gas, the product of its pressure and volume remains constant.

Let's understand with the help of an example: 

When you press a filled balloon with your hands, you reduce the space (volume) inside it. Since the air molecules now have less room to move, they collide more frequently with the inner surface of the balloon. As a result, the pressure inside the balloon increases.

 

What happens if you continue to squeeze? The pressure rises until the balloon bursts.
This is a simple yet perfect example of Boyle’s Law decrease in volume leads to an increase in pressure.

Let's have a look at the Derivation of Boyle’s Law Formula

Consider a gas that changes from an initial state (pressure } P_1, \text{ volume } V_1) to a final state (pressure } P_2, \text{ volume } V_2), while temperature remains constant.}

 

The fact that the product of a gas’s initial pressure and volume is equal to the product of its final pressure and volume, provided the temperature and the number of moles remain constant.

Since P \times V = k \text{ for both states, 

We can write the Boyle's law formula: 

 P1×V1=P2×V2. This is the mathematical expression of Boyle’s Law. Where,

P1=Initial pressure

V1=Initial volume

P2=Final pressure

V2=Final volume

Below is the Graphical Representation of Boyle's Law

If you plot Pressure (P) on the Y-axis and Volume (V) on the X-axis, the graph forms a curved hyperbola, showing an inverse relationship.

 

However, if you plot Pressure (P) against 1/V, the graph becomes a straight line, indicating direct proportionality between P and 1/V.

Real-Life Examples of Boyle’s Law

1. Breathing Process: When you inhale, the diaphragm moves downward, increasing lung volume and reducing air pressure inside. Air rushes in.

 

When you exhale, lung volume decreases, pressure rises, and air moves out, perfectly demonstrating Boyle’s Law.

2. Inflating a Balloon, Squeezing a balloon reduces its volume, causing internal air pressure to increase until it pops.

3. Syringe Action, have you ever noticed? Pulling back the plunger increases volume, lowers pressure, and draws liquid in. Pushing it down reduces volume, raising pressure and expelling the liquid.

4. Scuba Diving, As a diver ascends, the surrounding pressure decreases, causing air bubbles in the body to expand. This is why divers must rise slowly, Boyle’s Law in action for safety!

Also, students can check Charles' law for a better understanding of concepts.

Solved Example Problems

Example 1

A gas occupies a volume of 2 L at a pressure of 300 kPa. If the volume expands to 6 L, what is the new pressure?

P1=300 kPa, V1=2 L, V2=6 L

P1V1=P2V2

P2=P1V1V2=300×26=100 kPa

Final Answer: The new pressure is 100 kPa.

Example 2

A gas at 1 atm pressure has a volume of 500 mL. What will be the pressure if the volume is reduced to 250 mL, keeping the temperature constant?

P1=1 atm,V1=500 mL,V2=250 mL

P2=P1V1V2=1×500250=2 atm

Final Answer: The pressure becomes 2 atm when the volume is halved.

As we learned how Boyle’s Law beautifully explains the relationship between the pressure and volume of gases under constant temperature. It is a cornerstone concept in physics and chemistry that helps us understand natural phenomena and engineering systems from breathing to balloon flights.