**what is the Boyle’s law?**

The **law of** **Boyle or Boyle-Mariotte law** It is one that expresses the relationship between the pressure exerted by or on a gas, and the volume that it occupies; keeping constant both the temperature of the gas, as well as its quantity (number of moles).

This law, together with that of Charles, Gay-Lussac, Charles and Avogadro, describes the behavior of an ideal gas; specifically, in a closed container subjected to volume changes exerted by a mechanical force.

The image above briefly summarizes Boyle’s law. The purple dots represent gas molecules or atoms, which collide with the inner walls of the container (left). As the available space or volume of the container occupied by this gas decreases, collisions increase, which translates into an increase in pressure (right).

This shows that the pressure P and volume V of the gas are inversely proportional if the container is hermetically closed; otherwise, a greater pressure would be equal to a greater expansion of the container.

If you plotted V against P, with the data for V and P on the Y and X axes, respectively, you would see an asymptotic curve. The smaller V, the larger the increase in P; that is, the curve will continue towards high values of P on the X axis.

Of course, the temperature remains constant; but if the same experiment were performed at different temperatures, the relative positions of these V vs P curves would change on the Cartesian axis. The change would be even more apparent if it were plotted on a three-dimensional axis, with T constant on the Z axis.

**Boyle’s Law History**

**Background**

Since the scientist Galileo Galilei expressed his belief in the existence of a vacuum (1638), scientists began to study the properties of air and partial vacuums.

The Anglo-Irish chemist, Robert Boyle, began his study of the properties of air in 1638 upon learning that Otto von Guericke, a German engineer and physicist, had built an air pump.

**mercury experiment**

To carry out his studies of air pressure, Boyle used a glass tube in the shape of a «J», the construction of which was attributed to Robert Hooke, an assistant to Boyle. The short arm end was sealed, while the long arm end of the tube was open to place the mercury.

From the beginning, Boyle wanted to study the elasticity of air, qualitatively and quantitatively. By pouring mercury through the open end of the «J» tube, Boyle deduced that the air in the short arm of the tube was contracting under the pressure of the mercury.

**Results**

The greater the amount of mercury added to the tube, the greater the pressure exerted on the air and the smaller its volume. Boyle obtained a negative exponential type plot of the volume of air as a function of pressure.

Meanwhile, if you plot the volume of air against the inverse of the pressure, you have a straight line with a positive slope.

In 1662, Boyle published the first physical law that was given in the form of an equation, which indicated the functional dependence of two variables. In this case, the pressure and the volume.

Boyle pointed out that there was an inverse relationship between the pressure exerted on a gas and the volume that gas occupied, this relationship being relatively true for real gases. Most gases behave like ideal gases at moderate temperatures and pressures.

As higher pressures and lower temperatures occurred, deviations in the behavior of real gases from ideals became more noticeable.

**Edme Mariotte**

The French physicist Edme Mariotte (1620-1684) independently discovered the same law in 1679. But he had the merit of showing that volume varies with temperature. That is why it is called Mariotte’s law or Boyle and Mariotte’s law.

**Strengthening of the law**

Daniel Bernoulli (1737) strengthened Boyle’s law by pointing out that the pressure of a gas is produced by the impacts of the gas particles on the walls of the container that contain it.

In 1845, John Waterston published a scientific article, in which he focuses on the main principles of the kinetic theory of gases.

Subsequently, Rudolf Clausius, James Maxwell and Ludqwig Boltzmann consolidated the kinetic theory of gases, which relates the pressure exerted by a gas to the velocity of the moving gas particles.

The smaller the volume of the container that contains a gas, the greater the frequency of the impacts of the particles that form it against the walls of the container; and therefore, the greater the pressure exerted by the gas.

**What is this law about?**

The experiments carried out by Boyle indicate that there is an inverse relationship between the volume occupied by a gas and the pressure exerted on it. However, the indicated relationship is not completely linear, as indicated by a graph of variation of volume as a function of pressure attributed to Boyle.

Boyle’s law states that the volume occupied by a gas is inversely proportional to the pressure. It is also indicated that the product of the pressure of a gas by its volume is constant.

**Mathematic expression**

To arrive at the mathematical expression of Boyle’s law, we start from:

V ∝ 1/P

where indicates that the volume occupied by a gas is inversely proportional to its pressure. However, there is a constant that determines how inversely proportional this relationship is.

V = k/P

where k is the constant of proportionality. Solving what we have:

VP = k

The product of the pressure of a gas and its volume is constant. So:

V1P1 = k and V2P2 = k

And from this it can be deduced that:

V1P1 = V2P2

The latter is the final expression or equation for Boyle’s law.

**What is it for? What problems does Boyle’s law solve?**

**Steam engines**

The Boyle-Mariotte law is applied in the operation of steam engines. It is an external combustion engine that uses the transformation of the thermal energy of a quantity of water into mechanical energy.

Water is heated in a hermetically sealed boiler, and the steam produced exerts a pressure according to Boyle’s law that produces a volume expansion of a cylinder by pushing a piston.

The linear movement of the piston is transformed into a rotational movement, through the use of a system of connecting rods and cranks, which can drive the wheels of a locomotive or the rotor of an electric generator.

**slurping drinks**

The action of sucking a soft drink or juice from a bottle through a plastic tube is related to Boyle’s law. When air is sucked out of the tube using the mouth, there is a drop in pressure inside the tube.

This pressure drop facilitates the upward movement of the liquid in the tube, allowing it to be swallowed. This same principle works in drawing blood by using a syringe.

**Respiratory system**

Boyle’s law is closely related to the functioning of the respiratory system. During the inspiration phase, contraction of the diaphragm and other muscles occurs; for example, the external intercostals that produce an expansion of the ribcage.

This causes a decrease in intrapleural pressure, causing lung expansion that produces an increase in lung volume. Therefore, intrapulmonary pressure decreases in accordance with Boyle’s law.

As the intrapulmonary pressure becomes subatmospheric, atmospheric air flows into the lungs, causing increased pressure in the lungs; thus equalizing its pressure to atmospheric pressure, and concluding the inspiration phase.

Subsequently, the inspiratory muscles relax and the expiratory muscles contract. In addition, lung elastic retraction occurs, a phenomenon that produces a decrease in lung volume, with a consequent increase in intrapulmonary pressure, explainable by Boyle’s law.

As intrapulmonary pressure increases, and becomes greater than atmospheric pressure, air flows from inside the lungs to the atmosphere. This occurs until the pressures equalize, which concludes the expiration phase.

**References**

Boyle’s law. Encyclopædia Britannica. Recovered from: britannica.com

The Formula for Boyle’s Law. Retrieved from: thoughtco.com