Each tire of an automobile is equipped with a relief valve such that the pressur

Question

Each tire of an automobile is equipped with a relief valve such that the pressure inside the tire will not exceed 240 kPa (gage). A motorist starts a trip with a tire pressure of 200 kPa (gage) and an air temperature of 23?C in each tire. Initially, each tire contains 0.11 kg of air. During the long drive, the temperature of the air inside the tires reaches 83?C. (a) Determine the mass of air that escaped each tire over the course of the trip. (b) What will the tire pressure be when the air inside the tires (at end of trip) returns to 23?C? Hint: For part (a), you may assume the max pressure was reached (state 2), which allowed the air to escape.

Explanation / Answer

(a) intitally, Pi = 200 kPa Final pressure, Pf = 240 kPa Initial Temperature = Ti = 23o C = 296 K Final Temp, Tf = 83o C = 356 K Volume is constant. ? Mi *Ti/Pi = Mf *Tf /Pf => Mf = Mi * (Ti/Tf) * (Pf/Pi) = 0.11 * (296/356) * (240/200) = 0.1097 kg ? ?M = 2.47 *10-4 kg = 0.247 g (b) In this case the values of Ti, Tf, Pi will change: intitally, Pi = 240 kPa Final pressure, Pf = ? Initial Temperature = Ti = 83o C = 356 K Final Temp, Tf = 23o C = 296 K Volume is constant. and mass is constant. => Pi/Ti = Pf/Tf ? Pf = 240 * (296/356) = 199.55 kPa Pf = 199.55 kPa

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