Boyle's Law

Table of contents

1. Boyle's law definition
2. Boyle's law formula
3. Boyle's law example
4. Where is Boyle's law applied?
5. Other thermodynamic processes

Boyle's Law definition

Boyle's law tells us about the relationship between the pressure of a gas and it's volume at a constant temperature and mass of a gas. It states that the absolute pressure is inversely proportional to the volume.

Boyle's law describe the behavior of an ideal gas during an isothermal process, which means the temperature of a gas remains constant during the transition, as does the internal energy of a gas.

Boyle's Law formula

We can write the Boyle's law equation in the following way:

p₁ * V₁ = p₂ * V₂,

where p₁ and V₁ are initial pressure and volume respectively. Similarly, p₂ and V₂ are the final values of these gas parameters.

Depending on which parameter we want to estimate, Boyle's law formula can be written in various ways. Let's say we change the volume of a gas under isothermal conditions, and we want to find the resulting pressure. Then, the equation of Boyle's law states that:

p₂ = p₁ * V₁ / V₂ or p₂ / p₁ = V₁ / V₂.

As we can see, the ratio of the final and initial pressure is the inverse of the ratio for volumes.

 Boyle's Law graph

Boyle's example

A gas under 2.5 atm of pressure occupies 6 liters of space. It is then decompressed isothermally to the pressure of 0.2 atm. Find its final volume.

We have to rewrite the Boyle's law equation:

V₂ = p₁ * V₁ / p₂ =   2.5 atm * 6 l / 0.2 atm = 75 l.

Where is Boyle's law applied?

Boyle's law describes all processes for which temperature remains constant. In thermodynamics, temperature is a measure of the average kinetic energy that atoms or molecules have. 

There are a few areas where Boyle's law is applicable:

• Breathing also can be described by Boyle's law. Whenever you take a breath, your diaphragm and intercostal muscles increase the volume of your lungs, which results in the decrease of the gas pressure. As air flows from an area of higher pressure to an area of lower pressure, air enters the lungs and allows us to take in oxygen from the environment. During exhalation, the volume of lungs decreases, so the pressure inside is higher than outside, so the air flows in the opposite direction.
• Syringe - whenever you have to make an injection, a doctor or a nurse draws a liquid from the small vial first. To do so, they use a syringe. By pulling the plunger, the accessible volume increases, which results in the decrease of pressure, and, according to Boyle's law formula, causing the suction of the fluid.

Other thermodynamic process

Boyle's law, together with Charles's law and Gay-Lussac's law, are among the fundamental laws which describe the vast majority of thermodynamic processes.