Boyle’s law explains the relationship between the variables, pressure, and volume, at a constant temperature. The volume of a gas depends on different factors like temperature and pressure. The temperature has a direct while pressure has an inverse relation with the volume of a gas.

In 1660 Robert Boyle found a relationship between volume and pressure. There is a change in the volume of a gas with pressure. The volume of a gas increases with its decreasing pressure and vice versa.

Boyle’s law states that:

“At a constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure”.

This law was named after Robert Boyle who published it in 1662. It is also called Mariotte’s law because at that same time, a French physicist Edme Mariotte independently the same law in 1679.

## Mathematical Expression

The volume of gas is inversely proportional to the pressure of the gas keeping the temperature constant.

V ∝ 1/P

V = k x 1/P

where k is a proportionality constant.

PV = k

If P_{1 }and V_{1} are the initial pressure and volume of a gas, and P_{2 }and V_{2} are the changed pressure and volume. So we can write as:

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

- P
_{1}is the initial pressure exerted by the gas - V
_{1}is the initial volume occupied by a gas - P
_{2}is the final pressure exerted by the gas - V
_{2}is the final volume occupied by a gas

This relationship is very useful to determine the volume of any gas at any given pressure.

## Graphical Explanation of Boyle’s Law

A plot between volume and pressure for a given sample is a hyperbola that clearly depicts the inverse relationship between these quantities.

Similarly, a plot between volume and 1/P should be a straight line.

## Demonstration of Boyle’s Law

It is easy to demonstrate Boyle’s law. Simply take liquid mercury and a J-shaped glass tube. Add liquid mercury into the J-tube such that the mercury can clearly be seen. As you keep on adding mercury, the volume of the sample gas keeps on decreasing. It is because the pressure on the second gas increases by adding mercury. The pressure and volume of the gas are inversely proportional to each other. Hence, the volume of a system decreases as the pressure on it increases.

## Relation with KMT of gases and Ideal Gases

At moderate temperature and pressure, most gases behave like ideal gases. The 17th-century technology was very simple when scientists could not produce high pressures or low temperatures in their laboratories. Boyle’s law had just a few deviations at that time. Larger deviations started when new technologies were introduced with high pressures and low temperatures. These deviations of ideal gases are also known as gas deviation factors.

Theoretically, this law can be related to the assumptions of the kinetic molecular theory of gases. According to KMT, there are collisions between the molecules of gases. When high pressure is applied to a given sample of gas it increases the number of collisions and hence, its volume increases. If the volume is decreased, it will increase the collisions between gas molecules and eventually will increase the temperature as well.

## Applications of Boyle’s law

Boyle’s law is a fundamental gas law that is used to produce the Kinetic molecular theory (KMT) equation. Some of its applications are given as:

- Working on a medical syringe
- Inflating tires
- Paint sprays or aerosol sprays
- Breathing of humans and animals
- Packing of soda bottles
- Scuba diving
- Air pump
- Storage of gases, etc

**Additional articles:**

## Concepts Berg

**Can Boyle’s law be experimentally proven?**

Boyle’s law has many experimental applications in our daily life. So, it can be proven such as the working of a syringe, inflation of tires, breathing, etc. These applications are experimental shreds of evidence for Boyle’s law.

**What is a good example of Boyle’s Law?**

There are different examples of Boyle’s law in our daily life.

- Medical syringe
- Inflating tires
- Paints spray
- Breathing in humans and animals
- Packing of soda bottles, etc

**What is the formula for Boyle’s gas law?**

Boyle’s law states that at a constant temperature, the volume of the fixed mass of gas is inversely proportional to its pressure. It can be expressed as:

V ∝ 1/P

**Why is Boyle’s law important?**

Boyle’s law is an important gas law because it helps in the study of:

- Many experimental mechanisms.
- Derivation of the Kinetic Molecular Theory of gases.
- Low and high-pressure effects on liquids.

**How does Boyle’s law work?**

It explains the relationship between volume and pressure at a constant temperature. If the pressure of a gas increases, its volume decreases.

**What are the formulas used for Boyles’s Law?**

There are different formulas for Boyle’s law:

V ∝ 1/P

and

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

- P
_{1}is the initial pressure exerted by the gas - V
_{1}is the initial volume occupied by a gas - P
_{2}is the final pressure exerted by the gas - V
_{2}is the final volume occupied by a gas

**Why can’t we use Boyle’s law to extract energy from hot air?**

Boyle’s law does not explain the extraction of energy from hot air, it rather tells us how pressure and volume interact with each other at constant temperature.

**Does Boyle’s law obey the adiabatic process?**

No, it only obeys the isothermal process because the temperature is constant here.

**Reference Books**

**Chemistry |**Fifth edition, by**Steven S. Zumdhal**and**Susan A. Zumdhal**(**University of Illinois**, Urbana Champaign, IL, USA)

**Reference links**

- Boyle’s law (Wikipedia)
- Boyle’s law (britannica.com)
- What is Boyle’s law? (byjus.com)