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.
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?
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.
1 answer