The gauge pressure of an automobile tire is measured to be 190 kPa before a trip

Question

The gauge pressure of an automobile tire is measured to be 190 kPa before a trip and 215kPa afterwards. Atmospheric pressure is taken to be 95kPa. 1-if the tire walls are rigid, what is the nal temperature of the air in the tire if its initial temperature was 298K. 2- Assuming that the process is reversible, plot it in the (T; p) plane. 3-What is the eect of changing the initial temperature to 296K? or to 300K? .4- In the same gure, plot and label these transformations as well. All of these transformations are examples of what type of process? Note: that the thermodynamic pressure in the tire is the gage pressure plus the atmospheric pressure:e.g. p1= (190 + 95)kPa =285kP a .

Explanation / Answer

Since volume is constant

P/T = constant

P1/T1 = P2/T2

Also Pabs = Patm + Pgage

P1 = 95 + 190 = 285 kPa
P2 = 95 + 215 = 310 kPa
T1 = 273 + 25 = 298 K

=> T2 = (310 x 298) /285 = 324.14 K

= 324.14- 273 0C = 51.14 0C

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