How Does Temperature Affect the Pressure Inside a Football?

What happens to the gauge pressure inside a football when it is inflated at a higher temperature but used for play at a lower temperature?

Impact of Temperature on Gauge Pressure in a Football

When a football is inflated in a warm environment but later used in a colder setting, the gauge pressure inside the ball will decrease. This phenomenon can be explained by the ideal gas law, specifically Gay-Lussac's Law, which states that pressure is directly proportional to temperature when volume and amount of gas are constant.

Initially, when the football is pumped in the locker room at a temperature of 30°C, the air inside the ball expands as it warms up. The gauge pressure is measured at 13 psi under these conditions. However, when the football is taken outside for play at 5.0°C, the air inside the ball cools down and contracts.

As the temperature decreases, the molecules in the gas lose kinetic energy, resulting in fewer collisions with the walls of the ball. This decrease in collisions leads to a lower pressure inside the football. The relationship between pressure and temperature follows a direct proportionality as per Gay-Lussac's Law.

Therefore, after the football cools down to 5.0°C, the gauge pressure inside the ball is reduced to approximately 11.9 psi, based on the calculations derived from Gay-Lussac's Law.