Temperature Of the Air in a Tire

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Homework Help Overview

The discussion revolves around a problem involving the behavior of air in tires under varying temperatures and pressures. It specifically addresses the relationship between tire pressure and temperature changes during a drive, as well as the implications of releasing air from the tires.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculations related to tire pressure and temperature, particularly focusing on the confusion surrounding the expected gauge pressure after air is released and the temperature returns to its original state. There are attempts to clarify the relationship between pressure and temperature changes.

Discussion Status

The discussion is ongoing, with participants expressing confusion about the implications of the problem's conditions. Some have provided insights into the expected behavior of pressure when air is released, but there is no consensus on the reasoning behind the gauge pressure after cooling.

Contextual Notes

Participants are working within the constraints of the problem, which includes specific temperature and pressure values. There is a noted uncertainty regarding the interpretation of the pressure readings after air is let out and the subsequent cooling of the tires.

sona1177
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Homework Statement


Before starting out on a long drive, you check the air in your tires to make sure they are properly inflated. The pressure gauge reads 214 kPa and the temperature is 15 degrees celsius. After a few hours of highway driving, you stop and check the pressure again. Now the gauge reads 241 kPa. a) What is the temperature of the air in the tires now? b) Suppose you now (unwisely) decide to bleed air from the tires. If you let out enough air so that the pressure returns to 214 kPa, what percentage of the air molecules did you let out of the tires? c) What is the gauge pressure after the tires cool back to 15 degrees celsius?



Homework Equations


I figured parts a and b out. I am little confused what they mean in part c because isn't the pressure gauge at 15 degrees celsius 214 kPa? The answer is 189 kPa but I don't know why. Thanks.


The Attempt at a Solution


 
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sona1177 said:
I figured parts a and b out. I am little confused what they mean in part c because isn't the pressure gauge at 15 degrees celsius 214 kPa? The answer is 189 kPa but I don't know why. Thanks.

The idea is that, since you've let some air out of the tire in the previous step when the temperature is higher, when it cools back to the starting temperature (15 C) the pressure will drop below the original starting pressure.
 
Thanks but if I use the pressure when the temperature is higher and the the temperature when the pressure is lower, I end up with the samw gauge pressure given in the problem. I'm still confused :(
 
sona1177 said:
Thanks but if I use the pressure when the temperature is higher and the the temperature when the pressure is lower, I end up with the samw gauge pressure given in the problem. I'm still confused :(

You start with 15 deg C and 214 kPa.

When you stop you have T and 241 kPa. You have already stated you calculated T.

You let some air out and you have T and 214 kPa.

Now the temperature goes down to 15 deg C. Calculate new pressure knowing T, 214 kPa, and 15 deg C.
 

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