A motorist filled his tires to a pressure of 30.0 pounds per square inch (psi) at a temperature of a 27F. After a long drive, he found that the pressure had built up to 34.2psi. Estimate the temperature in Fahrenheit of the air tires. Assume that the tire gage reads relative pressure that the volume of the tires remains constant and that the ambient pressure is 1.00 atmosphere.
To estimate the temperature in Fahrenheit of the air in the tires, we can use the ideal gas law equation:
P1/T1 = P2/T2
Where:
P1 = initial pressure = 30.0 psi
T1 = initial temperature = 27°F + 460 (converting to Rankine) = 487 R
P2 = final pressure = 34.2 psi
T2 = final temperature = unknown
Converting the pressures to absolute units (atm):
P1 = (30.0 + 14.7) psi = 1.84 atm
P2 = (34.2 + 14.7) psi = 2.09 atm
Now we can plug these values into the equation:
1.84/487 = 2.09/T2
T2 = 2.09*487/1.84
T2 = 554.08 R
Converting the final temperature back to Fahrenheit:
T2 = 554.08 – 460 = 94.08°F
Therefore, the estimated temperature in Fahrenheit of the air in the tires after the long drive is approximately 94.08°F.