A bicycle tire is filled with air to a pressure of 6.80 atm and a temperature of 19 degrees Celsius. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58 degrees Celsius. The volume of the tire increases by 4.0%.What is the new pressure in the bicycle tire?
To find the new pressure in the bicycle tire, we can use the combined gas law, which relates the initial and final states of a gas sample. The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (unknown)
V2 = final volume (given)
T2 = final temperature
Let's plug in the given values into the equation and solve for P2:
P1 = 6.80 atm
V1 = volume before the temperature change (unknown)
T1 = 19 degrees Celsius + 273.15 (convert to Kelvin)
P2 = new pressure (unknown)
V2 = (1 + 4.0/100) * V1 (volume increase by 4.0%)
T2 = 58 degrees Celsius + 273.15 (convert to Kelvin)
First, let's convert the temperatures to Kelvin:
T1 = 19 + 273.15 = 292.15 K
T2 = 58 + 273.15 = 331.15 K
Now, let's rearrange the equation to solve for P2:
(P1 * V1 * T2) / (T1 * V2) = P2
Substituting the known values:
(6.80 * V1 * 331.15) / (292.15 * (1 + 4.0/100) * V1) = P2
Simplifying the equation:
(6.80 * 331.15) / (292.15 * 1.04) = P2
Using a calculator:
P2 ≈ 7.76 atm
Therefore, the new pressure in the bicycle tire is approximately 7.76 atm.