# Relationship between Pressure and Volume

In 1662, following research to understand the properties of air, Robert Boyle published some work that challenged the alchemical views of the the time period. Instead of seeing air as one of four mysterious “elements”, he saw it as a physical entity with knowable properties. His work gave us a clear understanding of the relationship between pressure and volume and has planted Boyle firmly into history as the father of modern chemistry.

For his experiment, Boyle use a glass tube sealed at one end. Varying amounts of mercury were added to vary the pressure of the system as he recorded the volume. The apparatus allowed Boyle to hold temperature and mass constant, and reduced the system to only two thermodynamic variables: pressure and volume.

This relationship between pressure and volume is known as “Boyle’s Law” and states that given a fixed mass and temperature, the ratio of pressure to volume in a system is constant. The mathematical expression is below, with V being the volume, P being the pressure and k being the gas constant that relates the units of these two properties.

Boyle’s Law: P x V = k

This relationship means that if the volume of the system increases, the pressure will inevitably decrease. If the system’s volume is decrease, the pressure must increase to compensate. This can be understood by kinetic theory, which holds that pressure is determined by the number of collisions between gases and the container that holds them. If you decrease the volume of a system, the gas is compressed and will have more contact with the walls of the container, increasing the pressure.

These variables can be further connected to temperature and mass through the Ideal Gas Law and the Combined Gas Law. Previously we were only considering pressure and volume, but these variables are directly proportional to the temperature of the system. For instance, if you increase the temperature of a system while holding the volume constant, the pressure will increase. But if we allow the volume to fluctuate, the system size will increase with increasing temperature, as shown in Boyle’s Law. This change in volume occurs to bring the pressure down, maintaining the ratio of these two values.

Resources:

Boyle’s Law at NASA.gov

Gas Laws: Georgia State University

Pressure and Temperature: University of Wisconsin at Madison

Boyle’s Law: Chemistry at Davidson College

Boyle’s Law: Montana State University

Gas Law Calculator at California State University