What would happen to a pressure gauge reading on a gas bottle if the gas were cooled?

When the gas in a bottle is cooled, the pressure gauge reading will show a lower reading due to the principles dictated by the gas laws, specifically Gay-Lussac's Law. This law states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. As the gas temperature decreases, its kinetic energy diminishes, leading to fewer collisions between gas molecules and the walls of the container. Consequently, this decrease in molecular activity results in reduced pressure within the bottle, which is reflected in the lower reading of the pressure gauge.