A car tire is inflated in the winter in Northern Wisconsin at -10.0F to a gauge
ID: 493295 • Letter: A
Question
A car tire is inflated in the winter in Northern Wisconsin at -10.0F to a gauge pressure of 32.4 PSI. The tire is rated to hold a maximum gauge pressure of 42.0 PSI. The owner is growing tired of the cold weather and decides to drive to San Diego for a holiday. During the trip, the owner decides to go through the Mojave Desert during an unseasonably warm day of 99.1F. Frequently, there are areas with no cell service and other cars may not pass for hours.
Does the driver need to worry about the tires? Assume each tire has a volume of 25.3L and does not leak. Will there be a problem with the tires?
(Yes/No)_______________ Provide calculations for the final gauge pressure of the tire in the dessert to support your choice.
Please show me details!
Explanation / Answer
NO.
Reason:
COnvert temperature ftom F to K,
K = ( F + 459.67) * (5 / 9)
Initial Temperature, T1 = ( - 10.0 + 459.67) * (5 / 9) = 249.82 K
Final Temperature, T2 = (99.1 + 459.67) * (5/9) = 310.43 K
Intial pressure, P1 = 32.4 PSI
Final pressure, P2 = ?
We know that,
P1 / T1 = P2 / T2
P2 = P1 * T2 / T1
P2 = 32.4 * 310.43 / 249.82
P2 = Final pressure = 40.26 PSI
It is given that, the tire has the maximum holding capacity of 42.0 PSI.
SO, there is no problem with the itre.
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