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Boyle's Law for Gases


Boyle's law for gases states that -

"At constant temperature, for a given sample of the gas, the pressure exerted by the gas is inversely proportional to the volume occupied by the gas."

The law was given by Robert Boyle in 1662.

We can see an explanation of the Boyle's law by the following argument. If a gas is confined into a small volume, the molecules of the gas experience more frequent collisions with the walls of the container. These frequent collisions increase the force that the walls of the container experience and hence there is an increase in the pressure exerted by the gas. This is shown in the following pictures.

boyle's law
Smaller Volume, more frequent collisions.


On the other hand, if the volume of the gas container is large for the same amount of the gas (at the same temperature), the molecules have more distance to travel and hence have relatively less collisions with the walls of the container. This reduces the force that the walls experience and hence the pressure exerted by the gas is less. Comparing the two pictures shows how the path available to the molecules increases with increase in volume of the gas and hence the pressure decreases.

boyle's law
Larger Volume, less frequent collisions.


In all these observations, temperature was to be kept constant because on changing the temperature of the gas, the speed of the gas molecules changes and the collision frequency is affected. If the temperature is increased, the gas molecules move faster and thus collide more frequently with the walls of the container, even in the same vessel.

Thus, if the volume occupied by the gas is large, the pressure exerted is less, and if the volume is small, the pressure exerted is more, keeping the temperature constant all the time, in accordance with the Boyle's law.

Boyle's law can be deduced from the ideal gas law also. The ideal gas law has the mathematical form -

PV = nRT

where,
P is the pressure exerted by the gas,
V is the volume occupied by the gas,
n is the number of moles of the gas,
T is the temperature of the gas.

This shows that if the temperature of the gas sample is kept constant, the right hand side of the equation is a constant and hence the right hand side is also a constant, that is, the product of Pressure and Volume of the gas is a constant and hence they are inversely proportional to each other.

Note that this result is valid only for the case of an ideal gas, where the size of the molecules and the interactions between them are neglected.

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