How to Derive Boyle's Law Using Kinetic Gas Equation

By Team Aakash Byju's

 Boyle’s law is a law that states that the pressure exerted by a gas varies inversely with its volume provided the temperature & mass of the gas are kept constant.

Let us see the mathematical representation of Boyle’s Law:

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The proportionality can be converted into an equation using a constant k.  Thus, P=k/V or PV=k.

According to the law, P is inversely proportional to V. 

The graphical representation of Boyle’s Law is shown below:

Now, let us derive Boyle’s Law using the kinetic gas theory equation.

According to kinetic gas theory, the pressure exerted by a gas is given as:

Where ρ is the density and v is the root mean square velocity of gas molecules.

For the above equation divide and multiply by 2 on RHS.

We know that density is the ratio of mass and volume(m/V), we substitute this in the equation for the pressure to get :

To get,

Therefore, we can write PV=2/3K.

We know that the kinetic energy of a gas molecule is given by the equation:

Now, if the temperature and mass of gas molecules are kept constant, their kinetic energy remains constant.

So k=constant, =>PV=constant at constant temperature and constant mass of gas.

Thus the kinetic gas equation concludes with Boyle’s Law. Add these points to your revision notes and share them with your friends.