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.
54497
how?
P1/t1=p2/t2
yeah that's right...p1/t1=p2/t2
don't forget to chaange units
LOL that's on brilliant
To find the gauge pressure inside the basketball when the temperature is 10°C, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
Since we want to find the gauge pressure, which is the difference between the absolute pressure inside the basketball and the atmospheric pressure, we can rewrite the equation as:
(P + Patm)V = nRT
Where:
Patm = atmospheric pressure (101,325 Pa)
First, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature:
T1 = 20°C + 273.15 = 293.15 K (initial temperature)
T2 = 10°C + 273.15 = 283.15 K (final temperature)
Now, we can solve for the final pressure (P2) by rearranging the equation:
(P2 + Patm)V = (P1 + Patm)V
P2 + Patm = P1 + Patm
P2 = P1
Therefore, the final gauge pressure inside the basketball would be equal to the initial gauge pressure.
The initial gauge pressure is given as 60,000 Pa. Hence, the gauge pressure inside the basketball when the temperature is 10°C would also be 60,000 Pa.
Note: The reason basketballs tend to get flat in cold weather is due to the decrease in air temperature. As the temperature drops, the air inside the basketball cools and contracts, resulting in a decrease in air pressure. This decreased pressure causes the basketball to appear flat.