# Boyle’s Law

Boyle’s law is an experimental gas law that explains the relationship between pressure and volume. According to Boyle’s law, the pressure and volume are inversely proportional, provided the temperature and mass remain unchanged ^{[1-4]}.

The law was named after Anglo-Irish physicist and chemist Robert Boyle, who published the law in 1662.

## Equation

Suppose P is the pressure and V is the volume of the gas. Mathematically, Boyle’s law is given by ^{[1-6]}

P ∝ 1/V

Or, P = k/V

Or, PV = k

Where

P : Pressure

V : Volume

k : Proportionality constant

This equation states that the product of pressure and volume is a constant for a given mass confined to a container as long as the temperature remains unchanged. A graphical representation of the above equation is shown below.

Boyle’s law can be used to establish a relationship between two states of a gas. Suppose the gas with pressure P_{1} and volume V_{1} expands or shrinks to pressure P_{2} and volume V_{2}. Then, using Boyle’s law equation,

P_{1}V_{1} = k and P_{2}V_{2} = k

From the above two equations

P_{1}V_{1} = P_{2}V_{2}

This equation shows that as the pressure increases, the volume decreases and vice versa. For example, when the pressure doubles, the volume is decreased by half. Also, the units of pressure and volume must be consistent. P_{1} and P_{2} must be expressed in Pa or atm. V_{1} and V_{2} must be expressed in m^{3} or L.

## Examples

Here are some examples of Boyle’s law in real life ^{[3]}.

**Respiration and Breathing**: When we inhale, our lungs expand. As a result, the volume increases, and pressure decreases. The air pressure inside the lungs is less than the environmental pressure. Hence, oxygen from the environment fills up the lungs. The reverse happens during exhalation. When we exhale, the lungs shrink. Its volume decreases, and pressure increases. The air pressure inside the lungs is higher than the environmental pressure. Hence, the air is expelled out of the lungs.

**Syringe**: A syringe draws liquid from a small vial and injects it into a body. It consists of a barrel, needle, and plunger. When the plunger is pulled, the volume inside the barrel increases, resulting in a decrease in pressure. Any fluid flows from high pressure to a low-pressure region. Since the pressure outside the syringe, near the needle, is higher than the pressure inside it, fluid will flow into the syringe. The reverse also holds. When the plunger is pushed, it creates a low volume and high pressure inside the syringe. As the pressure inside is higher than outside, the fluid will flow out of the syringe.

**Balloon**: When a balloon filled with air is squeezed, its volume decreases, and pressure increases. If the balloon is squeezed further, the pressure inside the balloon is so high that it causes the balloon to burst.

## Problems and Solutions

**Problem 1**: A gas confined to a volume of 2 L at a pressure of 10 atm. It can flow into a 10 L container by opening the valve that connects the two containers. What is the final pressure of the gas?

**Solution**:

Given

P_{1} = 10 atm

V_{1} = 2 L

V_{2} = 10 L

From Boyle’s law,

P_{1}V_{1} = P_{2}V_{2}

Or, P_{2} = P_{1}V_{1}/ V_{2}

Or, P_{2} = 10 atm x 2 L/ 10 L

Or, P_{2} = 2 atm

**Problem 2**: A gas exerts a pressure of 5 kPa on the walls of a container. When the container is emptied into a 12 L container, the pressure exerted by the gas increases to 8 kPa. Find the volume of container 1.

**Solution**:

Given

P_{1} = 5 kPa

P_{2} = 8 kPa

V_{2} = 12 L

From Boyle’s law,

P_{1}V_{1} = P_{2}V_{2}

Or, V_{1} = P_{2}V_{2}/P_{1}

Or, V_{1} = 8 kPa x 12 L/5 kPa

Or, V_{1} = 19.2 L

## FAQs

**Q.1. What are the variables of Boyle’s law?****Ans.** The variables involved in Boyle’s law are pressure and volume. On the other hand, temperature and the number of moles of gas are the constants.