Boyle's law calculator

What is Boyle’s law?

Boyle’s law is a fundamental principle of physics that finds applications in various fields of science and engineering. It describes how the pressure of a gas changes with variations in its volume at a constant temperature. Formally, Boyle’s Law states that the product of a gas’s pressure and volume remains constant if the temperature and number of gas molecules are fixed. This can be expressed using the formula:

$P \times V = \text{const}$

where $P$ is the pressure of the gas and $V$ is its volume.

Understanding this law explains why car tires become stiffer when air is pumped into them or how pistons work in an engine.

If you’re interested in exploring more about physics or need specific calculations for your activities, you should visit our section on other physics calculators.

History of Boyle’s law

This law was first discovered in the mid-17th century by the English physicist and chemist Robert Boyle. While studying the properties of gases, he discovered that as the volume of a gas decreases, its pressure increases, and vice versa. These findings were published in his work “New Experiments Physico-Mechanical, Touching the Spring of the Air and its Effects.”

Boyle’s law or Boyle-Mariotte law?

The formula $PV = \text{const}$, which describes the inverse relationship between the pressure and volume of a gas at constant temperature, is known as Boyle’s law. However, this equation is sometimes also referred to as the Boyle-Mariotte law. The reason is that around the same time Robert Boyle was conducting his experiments in England, French physicist Edme Mariotte was working on similar research in continental Europe. Although his work was published later than Boyle’s, Mariotte’s discovery also contributed to the understanding of gas behavior and the applicability of this law.

Mariotte experimentally confirmed Boyle’s results independently and, thanks to his research, this law became widely known in scientific circles in Europe. Therefore, in some countries, especially French-speaking ones, the law is often named after both scientists—Boyle and Mariotte.

Various units of pressure measurement

Pressure, as a physical quantity, can be measured in different units. The most commonly used are:

• Atmospheres (atm): used to describe the average pressure of the atmosphere at sea level.
• Pascals (Pa) and Kilopascals (kPa): the primary SI unit where 1 atm ≈ 101325 Pa.
• Millimeters of Mercury (mmHg): a traditional unit frequently used in medicine.
• Bar: a technical unit equal to 100 kPa.

Understanding and converting between these units is essential, especially in technical and scientific applications, to avoid errors.

Related topics

Ideal gas

Boyle’s law is part of a more comprehensive theory—the ideal gas law. An ideal gas is a hypothetical model where a gas is considered as a collection of non-interacting molecules that collide elastically. The equation for such a gas is:

$PV = nRT$

where $n$ is the number of moles of gas, $R$ is the universal gas constant, and $T$ is the temperature in Kelvin.

Gay-Lussac’s law

Another law related to the behavior of gases is Gay-Lussac’s law, which states that at constant volume, the pressure and temperature of a gas are directly proportional:

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Formula

The primary formula of Boyle’s law:

$P_1 \times V_1 = P_2 \times V_2$

If the initial volume and pressure of a gas are known, and one of these parameters changes, you can easily find the other using a Boyle’s law calculator. For instance, knowing the initial and final pressures, we can find the volume change.

Examples

1. Volume calculation example:

   Suppose there is a gas at a pressure of 2 atm in a volume of 3 liters, and its pressure increases to 3 atm. What is the new volume of the gas?

   Using Boyle’s law formula:

   $$P_1 \times V_1 = P_2 \times V_2$$

   Substituting the values, we get:

   $$2 \, \text{atm} \times 3 \, \text{L} = 3 \, \text{atm} \times V_2$$

   Solving the equation, we find:

   $$V_2 = \frac{6}{3} = 2 \, \text{L}$$

   Thus, the new volume of the gas is 2 liters.

2. Pressure calculation example:

   If initially, a gas occupies a volume of 10 liters at a pressure of 1.5 atm, and the volume changes to 5 liters, what will be the gas pressure?

   Substituting values into the formula:

   $$1.5 \, \text{atm} \times 10 \, \text{L} = P_2 \times 5 \, \text{L}$$

   We get:

   $$P_2 = \frac{15}{5} = 3 \, \text{atm}$$

   The pressure of the gas will increase to 3 atm.

3. Application example on car tires:

   Consider a scenario where a car tire holds 30 liters of air at 2 atm pressure. The car is loaded, and the tire deflates to a volume of 28 liters. We need to calculate the new tire pressure.

   $$P_1 \times V_1 = P_2 \times V_2$$ $$2 \, \text{atm} \times 30 \, \text{L} = P_2 \times 28 \, \text{L}$$ $$P_2 = \frac{60}{28} \approx 2.14 \, \text{atm}$$

   The pressure in the tire will increase to approximately 2.14 atm. This calculation can help drivers assess whether tire pressure is sufficient for safe vehicle operation, especially when the load increases.

Notes

• Boyle’s law applies only under ideal conditions where the temperature remains unchanged.
• It is well-suited for dilute gases in large volumes, whereas at high pressures or low temperatures, deviations may occur.

Frequently asked questions

How to find gas pressure if the volume doubles, and the initial pressure is 4 atm?

With a doubled volume and constant temperature, the pressure will halve according to Boyle’s Law:

$P_2 = \frac{1}{2} \times P_1 = \frac{1}{2} \times 4 \, \text{atm} = 2 \, \text{atm}$

Is Boyle’s law applicable in space?

Yes, in space conditions where rarefied gases are often considered, it can be quite useful, though many other factors may influence specific conditions.

What other gas laws are known?

Apart from Boyle’s law, Charles’s law and Gay-Lussac’s law are famous, which are part of the Ideal Gas Law, addressing various conditions affecting temperature and volume changes.

Why doesn’t Boyle’s law work at high pressures?

At high pressures, molecules begin to interact, affecting the ideal gas behavior, making the law less accurate.

Is Boyle’s law used in industry?

Yes, Boyle’s law is applied in designing engines, life-support systems, compressors, and expansion tanks.

How does temperature affect Boyle’s law results?

Boyle’s law presumes constant temperature. If the temperature shifts, more complex models like the Ideal Gas Law are necessary for computations.