A motorist filled his tires to a pressure of 30.0 pounds per square (psi), he that the pressure had built up to 34.2 psi. Estimate the temperature (in °F) of the air in the 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.

Answer 1

To estimate the temperature of the air in the tires, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure in atmospheres
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin

Since the volume and the number of moles remain constant, we can rewrite the equation as:

P1/T1 = P2/T2

Where:
P1 = initial pressure (30.0 psi + 1 atm = 2.07 atm)
T1 = initial temperature in Kelvin (let's assume 300K)
P2 = final pressure (34.2 psi + 1 atm = 2.23 atm)
T2 = final temperature in Kelvin

Now we can plug in the values and solve for T2:

(2.07 atm) / 300K = (2.23 atm) / T2

2.07T2 = 669
T2 = 323.4K

Finally, we convert the temperature to Fahrenheit:

T(°F) = T(K) * 9/5 - 459.67
T(°F) = 323.4 * 9/5 - 459.67
T(°F) = 584.12°F

Therefore, the estimated temperature of the air in the tires is approximately 584.12°F.