Boyle’s law: pressure-volume relationship in gases

STATEMENT:

The Boyle’s Law states that 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.

Mathematically it can be written as:

$P \propto \frac {1}{V}$

The graph of $P$ against $V$ is as below:

As the volume increases the pressure decreases and vice versa

The graph of $P$ against $\frac {1}{V}$ is as below:

The graph of $P$ against $\frac {1}{V}$ is a straight line that passes through the origin.

DERIVATION:

As $P \propto \frac{1}{V}$

Replacing the proportionality sign and adding the constant the relationship becomes:

$P = \frac {k}{V}$

or

$P V = k$

Meaning that the product between the Pressure and Volume of a gas is constant given that the mass and the temperature of the gas remain constant.

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 mass).

If Initial pressure and volume of a gas are taken as $P_1$ and $V_1$,then we can say:

${P_1V_1=k}$

And if the final pressure and volume of a gas are taken as $P_2$ and $V_2$, we can say:

$P_2V_2=k$

Therefore we can say that:

$\boxed {P_1V_1= P_2V_2}$

Examples

Bicycle Pump

A bicycle pump is good example of Boyle’s law. As the volume of the air trapped in the pump is

reduced, its pressure goes up, and air is forced into the tyre.

Breathing:

One important demonstration of Boyle's law is our own breathing. Inhaling and exhaling basically means increasing and decreasing the volume of our chest cavity. This creates low pressure and high pressure in our lungs, resulting in air getting sucked into our lungs and leaving our lungs.

Aerosols:

Aerosols, such as spray paints, use the Boyle’s law in their working mechanism