Gay-Lussac's Law

Gay-Lussac's Law (Pressure and Temperature relationship, V constant)

In this law, we will look at how Pressure 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 round bottom flask is heated. As the temperature of the gas increases, the pressure increases, as shown by the pressure gauge. 

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

 As can be seen from the graph above, when plotted using the Celsius scale, a very similar to the Charles' law graph is generated with the intercept on the x axis of absolute zero. 

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

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

where:-

P1 = Pressure at start.

T1 = Temperature at start.

P2 = Pressure at end.

T2 = Temperature at end.

The video below gives a short summary of Gay-Lussac's Law:-

Example 1 - 

A diver uses a rigid scuba tank to remain underwater for long periods of time. The temperature at the sea's surface is 300 K and the temperature at a depth of 40m is 290 K. If the tank's pressure at the surface is 20x105 Pa, what is the pressure at operating depth?

P1 = 20x105 Pa

T1 = 300 K

P2 = ? 

T2 = 290 K

P1 / T1  =  P2 / T2

20x105 / 300  =  P2 / 290

P2 = 1.93x105 Pa

P2 = 193 kPa

Kinetic Theory Explanation of Gay-Lussac's 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 applied to the walls gives a larger pressure.