Question

The gage pressure of an automobile tire is measured to be 210kPa before a trip and 220kPa after the trip at a location where the atmospheric pressure is 95kPa. Assuming the volume of the tire remains constant and the air temperature before the trip is 25o C, determine the air temperature in the tire after the trip. (

Answer 1

Answer:

$T_{f} = 312.348\,K\,(39.198\,K)$

Explanation:

Let assume that gas inside the automobile tire behaves as an ideal gas. Due to the absence of leakages, the number of moles remains constant during the trip. Air temperature can be found by using the following relation:

$\frac{P_{o}}{T_{o}}=\frac{P_{f}}{T_{f}}$

Final temperature is cleared with the expression:

$T_{f} = \frac{P_{f}}{P_{o}}\cdot T_{o}$

$T_{f} = \frac{220\,kPa}{210\,kPa}\cdot (298.15\,K)$

$T_{f} = 312.348\,K\,(39.198\,K)$