Charles' Law

Charles' Law (Volume and temperature relationship, P constant)

In this law, we will look at how Volume and Temperature are related for a fixed mass of gas in a sealed container.

In the above diagram, a fixed mass of gas within a piston is heated. As the temperature of the gas increases, the volume increases, pushing the piston upwards.

If we plot a graph of volume against temperature for the piston above we would generate the graph below:-

As can be seen from the graph above, when plotted using the Celsius scale, a proportional graph is generated. However, this graph is not directly proportional (doubling temperature does not double volume).

If the intercept on the x axis is found, however, it is shown to be the same value no matter the gas - absolute zero:-

Therefore, in order to generate a directly proportional graph, the Kelvin scale must be used:-

This graph does follow a linear relationship, which shows that:-

Where:-

V1 = Volume at start.

T1 = Temperature at start.

V2 = Volume at end.

T2 = Temperature at end.

The video below gives a short summary of Charles' Law:-

Example 1 -

A weather balloon is held at a constant pressure of 1 atmosphere before launch, with a volume of 4 m3. The temperature of the balloon when first inflated was 12 °C. By the time of launch the balloon's temperature had increased to 28 °C, what is the new volume of the balloon?

V1 = 4 m3

T1 = 12 °C = 12 + 273 = 285 K

V2 = ?

T2 = 28 °C = 28 + 273 = 301 K

V1 / T1 = V2 / T2

4 / 285 = V2 / 301

V2 = 4.2 m3

Kinetic Theory Explanation of Charles' Law

When a gas is Heated:-

1. The gas particles have greater Kinetic Energy.

2. The particles will collide with the container walls more often.

3. Higher rate of collisions gives a larger Force applied to the walls.

4. Larger force gives pushes out the walls of the container giving a bigger volume.