Robert Boyle proposed Boyle’s Law in 1662. Boyle’s law is a gas law which states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.

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## What is Boyle’s Law?

This law was established by Robert Boyle in 1662.

**At constant temperature, the absolute pressure of a given mass of a perfect gas is inversely proportional to its volume.**

Have you understand something from this? If not than let’s we understand what this statement implies. It means that if we have a perfect gas of a given mass at constant temperature (i.e. the temperature which stays unchanged throughout the change of state of the gas), and if the pressure of the gas will increase than the volume of the gas decreases and if the pressure decreases than the volume of the gas will increase. So the conclusion is that the pressure varies inversely to

its volume at constant temperature for a really perfect gas.

Mathematically

Here the suffixes 1, 2, 3 represents different sets of conditions.

## Formula and Derivation

As per Boyle’s law, any change in the volume occupied by a gas (at constant quantity and temperature) will result in a change in the pressure exerted by it. In other words, the product of the initial pressure and the initial volume of a gas is equal to the product of its final pressure and final volume (at constant temperature and number of moles). This law can be expressed mathematically as follows:

**P _{1}V_{1} = P_{2}V_{2}**

Where,

- P
_{1}is the initial pressure exerted by the gas - V
_{1}is the initial volume occupied by the gas - P
_{2}is the final pressure exerted by the gas - V
_{2}is the final volume occupied by the gas

This expression can be obtained from the pressure-volume relationship suggested by Boyle’s law. For a fixed amount of gas kept at a constant temperature, PV = k. Therefore,

**P _{1}V_{1} = k **(initial pressure * initial volume)

**P _{2}V_{2} = k **(final pressure * final volume)

**∴ P _{1}V_{1} = P_{2}V_{2}**

This equation can be used to predict the increase in the pressure exerted by a gas on the walls of its container when the volume of its container is decreased (and its quantity and absolute temperature remain unchanged).

## Example of Boyle’s Law

To understand this law more clearly let’s take an example. Suppose we have a system of cylinder piston association wherein a really perfect gas of given mass is present and the piston is free to slide in the cylinder. Let the system is location at room temperature and initially P1, V1 be the pressure and volume of the gas. Now start putting some sand gradually on the top a part of piston. What you’ll see from this, you’ll observe that the pressure at the piston will increase and so the pressure and this pushes the piston downward.

The piston starts moving downward results in decrease of the volume. Here the increase in pressure results in decrease in volume. Now start removing the sand gradually, since we are removing the sand, so we’re reducing the pressure on the gas. This time we see that the piston movements upward and the volume of the gas will increase. From this the conclusion comes out is that as the pressure on the gas will increase its volume decreases and when pressure on the gas decreases than the volume will increase.

In the above example if we calculate the value of PV in every case, we can get the same solution i.e. 20.

**Note:** Since the system is at room temperature so the temperature of the system remains constant ( T = 298 K) in every state change. A confusion arises with that, how this temperature remains constant when we compresses the gas because on compression the temperature should be increases. Yes your confusion is right. As the piston gradually compresses the gas, the temperature of the gas increases but the extra increases in temperature is rejected to the surrounding as heat through the conducting walls the cylinder. And the temperature of the gas remains unchanged.

The above example proves the statement of the Boyle’s law.

## Graph

The various graph of the Boyle’s law is given below: