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How many air molecules are there inside the tire?

  • #1
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Homework Statement



A car tire has a volume of 10 L and is inflated to a gauge pressure of 30 psi (207,000 Pa) at 20°C. How many air molecules are there inside the tire?


Homework Equations


N = PV/ kbT

The Attempt at a Solution



(207,000 Pa )x (0.01 m3) / (1.38 x 10^-21 x 293) =5.12 x 10^23

However, my instructor's answer is:
( 101,000 + 207,000 Pa )x(0.01 m3) / (1.38 x 10-21 x 293) = 7.6 x 10^23

Where is he getting that extra 101,000 that he is adding to the pressure??
 

Answers and Replies

  • #2
haruspex
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Where is he getting that extra 101,000 that he is adding to the pressure??
Gauge pressure means the pressure that would be shown on a standard pressure gauge. That would be relative to ambient pressure. For the calculation you need absolute pressure, so atmospheric pressure must be added.
 
  • #3
Nathanael
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30 psi is the gauge pressure. A gauge under atmospheric pressure reads zero.

Edit: oops haruspex said it first
 
  • #4
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A gauge pressure of 30 psi means an absolute pressure of 30+14.7= 44-7 psi. The ideal gas law uses the absolute pressure, not the gauge pressure.
 

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