Boyle's Law (Pressure and Volume relationship, T constant)
In this law, we will look at how Pressure and Volume are related for a fixed mass of gas in a sealed container.
The video below demonstrates Boyle's law when applied to several everyday objects:-
In the above diagram, gas is trapped within a piston. When the piston is pushed in, the gas is compressed giving a high pressure. As the piston is released, the volume increases and the pressure decreases.
If we plot a graph of pressure against volume for the piston above we would generate the graph below:-
Obviously this graph does not show a linear relationship, however, if we plot a graph of Pressure against 1 / Volume we would generate the following:-
This graph does follow a linear relationship, which shows that:-
P1 = Pressure at start.
V1 = Volume at start.
P2 = Pressure at end.
V2 = Volume at end.
The video below gives a short summary of Boyle's Law:-
A Piston in a car moves up and down in a cylinder. When the piston is extended, the volume is 200 ml and the pressure is 1.013x105 Pa. When the piston is compressed, the volume is reduced to 25 ml. What is the new pressure inside the piston, assuming the temperature is constant?
P1 = 1.013x105 Pa
P2 = ?
V1 = 200 ml
V2 = 25 ml
P1 x V1 = P2 x V2
1.013x105 x 200 = P2 x 25
P2 = 2.026x107 / 25
P2 = 8.104x105 Pa
P2 = 0.8104 MPa
Kinetic Theory Explanation of Boyle's Law
When a gas is compressed:-
1. The volume that the gas occupies is decreased.
2. The gas particles will collide with the walls of the container more often.
3. Higher rate of collisions gives a larger Force applied to the walls.
4. Larger force gives a higher pressure.