The relationship between temperature and pressure in a vacuum system is described by the ideal gas law. According to the ideal gas law, the pressure of a gas is directly proportional to its temperature when the volume and the number of gas molecules are constant. This relationship can be expressed mathematically as:

P ∝ T

Where:

P is the pressure of the gas

T is the temperature of the gas

In simpler terms, as the temperature of a gas in a vacuum system increases, the pressure of the gas also increases. Conversely, when the temperature decreases, the pressure decreases as well.

It is important to note that this relationship holds true when the volume and the number of gas molecules remain constant. If the volume or the number of gas molecules changes, the relationship between temperature and pressure may become more complex. However, in a vacuum system where the volume is typically constant, the direct proportionality between temperature and pressure is a useful approximation.

Source: HyperPhysics: Ideal Gas Law  –  http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/idegas.html