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:-
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:-
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.