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3 years ago

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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. (

1 answer:

Katarina [22]3 years ago

7 0

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:

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

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

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

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$\vec{F} = - k \Delta \vec{x}$

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$k = \frac{9.12 \ N}{4.6 \ 10^{-2} \ m}$

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<h3>Gravitational potential energy</h3>

To see how much gravitational potential energy will the pellet win, we can use

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where m is the mass of the pellet, g is the acceleration due to gravity and \Delta h is the difference in height.

Taking all this together, the gravitational potential energy when the spring is relaxed will be:

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We know that the kinetic energy for a mass m moving at speed v is:

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so, for the pellet will be

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