A bicycle tire is filled with air pressure of 6 atm at a temperature 20 Degrees Celsius. Riding the bicycle on asphalt on a hot day at a temperature 42 degrees Celsius makes the volume of the tire increase by 2%.
What is the new pressure in the bicycle tire?
To calculate the new pressure in the bicycle tire, we need to use the combined gas law equation:
(P1 * V1) / (T1 + 273) = (P2 * V2) / (T2 + 273)
Where:
P1 = initial pressure (in atm)
V1 = initial volume (in liters)
T1 = initial temperature (in Celsius)
P2 = final pressure (in atm)
V2 = final volume (in liters)
T2 = final temperature (in Celsius)
Given:
P1 = 6 atm (initial pressure)
T1 = 20°C (initial temperature)
T2 = 42°C (final temperature)
V2 = V1 + 0.02 * V1 (The volume increases by 2%)
First, let's convert the temperatures to Kelvin:
T1 (in Kelvin) = T1 (in Celsius) + 273 = 20 + 273 = 293K
T2 (in Kelvin) = T2 (in Celsius) + 273 = 42 + 273 = 315K
Next, substitute the given values into the equation:
(6 * V1) / (293) = (P2 * (V1 + 0.02 * V1)) / (315)
Simplifying the equation:
6 / 293 = (P2 * (1 + 0.02)) / 315
Now, solve for P2:
P2 = (6 / 293) * (1 + 0.02) * 315
Calculating the value of P2:
P2 ≈ 6.254 atm
Therefore, the new pressure in the bicycle tire is approximately 6.254 atm.