Understanding Boyle’s Law | Mariotte’s Law: Comprehensive Guide, Calculator, and Historical Insights

April 28, 2024

Why Is Boyle’s Law Also Called Mariotte’s Law?

Boyle’s Law, named after the Anglo-Irish physicist Robert Boyle, who published his findings in 1662, is one of the earliest descriptions of the behaviour of gases under varying pressures

In France, the physicist Edme Mariotte independently discovered the same principle around 1676, nearly 14 years after Boyle’s publication. Mariotte did more to expand upon the law, noting that the pressure-volume relationship he observed only proved to be true at constant temperatures. In acknowledgment of his contributions, the law is known as Mariotte’s Law in many parts of Europe, especially France.

Some refer to the name as the Boyle-Mariotte Law acknowledging both of the physicists work and contribution to this Law.

What Is Boyle’s Law / Mariotte’s Law?

Boyle’s law, also referred to as the Boyle-Mariotte law, outlines the inverse relationship between the pressure and volume of a gas, provided that the temperature and the mass of the gas remain constant. Essentially, it states that the absolute pressure of a gas inversely correlates with its volume.

Another way to express Boyle’s law is to say that in a sealed system, the product of the pressure and volume of a gas remains constant if the temperature does not vary.

This law is applicable to an ideal gas, which is described by the ideal gas equation. Boyle’s law focuses on isothermal processes, indicating that both the temperature and the internal energy of the gas stay stable throughout the process.

Boyle’s Law Formula | Mariotte’s Law Formula

As said previously, Boyle’s law describes the relationship between the pressure and volume of a gas under constant temperature conditions. The formula for Boyle’s law is generally represented as:

p_1V_1 = p_2V_2

where p1 and V1 represent the initial pressure and volume of the gas, and p2 and V2 represent the final pressure and volume after changes under the same temperature.

The Boyle’s law equation can be changed depending on the variable you need to solve for. For instance, if the volume of a gas is changed while maintaining isothermal conditions, and you need to determine the final pressure, the equation can be rearranged as:

P_1 = \frac{p_1 V_1}{V_2}


\frac{P_1}{P_2} = \frac{V_1}{V_2}

As you may notice from the equations above, the ratio of the final and initial pressure is the inverse of the ratio for volumes.

To help with understanding, Boyle’s law can be visualised through a graph that illustrates how pressure varies inversely with volume at a constant temperature. This graph usually features a hyperbolic curve, indicating whether the gas is compressed or expanded, the relationship defined by Boyle’s law holds true.

A representation of Boyle’s Law combined with a graph (Credit: NASA)

Boyle’s Law Calculator

Boyle’s Law can be seen used in several real world applications, covering scenarios from laboratory experiments to engineering applications. A Boyle’s law calculator simplifies calculations by allowing you to input any three of the four parameters (initial and final volumes and pressures), and automatically computes the fourth. This tool demonstrates the law’s utility and how it governs the behaviour of gases in various settings, both natural and engineered.

Boyle’s Law Uses In Real World Applications and Industry

Boyle’s law applies to processes where the temperature remains constant. Thermodynamically, temperature is the average kinetic energy of atoms or molecules, this means that the average speed of gas particles remains unchanged during these processes. The formula for Boyle’s law holds across various temperature ranges.

Boyle’s law has several practical applications:

  1. Carnot Heat Engine – This engine operates through four thermodynamic processes, including two isothermal processes that adhere to Boyle’s law. This is key to determining the maximum efficiency possible for any heat engine.
  2. Respiration – Boyle’s law explains the mechanics of breathing. Inhalation occurs when the diaphragm and intercostal muscles expand the lungs, reducing the internal gas pressure and causing air to flow inward from a region of higher external pressure. The opposite of this, exhalation compresses the lungs, increasing internal pressure and forcing air out.
  3. Syringe Use – When a doctor or nurse pulls back the plunger, it increases the volume inside the syringe, reducing the pressure and creating suction that draws fluid into the syringe, according and adhering to Boyle’s law.

These examples highlight how Boyle’s law is instrumental in various fields, from engineering to healthcare, by describing how gases behave under constant temperature conditions.

If you would like to know more about Boyle’s Law or you are more of a auditory and visual learner, here is a video that we think sums up Boyle’s Law perfectly.

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