Many of you may have noticed the phenomenon that basketballs get flat if the weather is cold. If a basketball was inflated to a gauge pressure of 60,000 Pa when the temperature outside was 20∘C, what is the gauge pressure inside the basketball in Pa when the temperature is 10∘C?

Question

Details and assumptions
The outside air maintains a constant pressure of 1 atm=101,325 Pa as the temperature changes.
The basketball always has a circumference of 0.75 m.
There's a reason gauge is in bold face. If you don't know what gauge pressure is, you should look it up before attempting the problem.

Answer 1

At 60,000 Pa gauge pressure, the absolute pressure inside the ball is
101,325 + 60,000 = 161,325 Pa

Dropping the absolute temperature from 293 to 283 K decreases the absolute pressure in the ball by a factor 283/293, resulting in 15,582 Pa. Subtract ambient pressure from that for the new gauge pressure. The gauge pressure becomes 54,494 Pa.