Temperature Of the Air in a Tire

AI Thread Summary
The discussion revolves around calculating the temperature of air in tires after a long drive, where initial conditions are 214 kPa at 15 degrees Celsius, increasing to 241 kPa during driving. The confusion arises regarding the pressure after bleeding air back to 214 kPa and how it relates to the temperature drop back to 15 degrees Celsius. It is clarified that when the air cools, the pressure will drop below the original 214 kPa due to the loss of air molecules during bleeding. The expected gauge pressure after cooling is 189 kPa, which is lower than the initial reading. Understanding the relationship between temperature, pressure, and volume in tires is essential for accurate calculations.
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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