How many air molecules are there inside the tire?

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SUMMARY

The discussion centers on calculating the number of air molecules in a car tire with a volume of 10 liters and a gauge pressure of 30 psi (207,000 Pa) at 20°C. The correct formula to use is N = PV/kbT, where absolute pressure must be considered. The instructor's calculation includes atmospheric pressure, resulting in an absolute pressure of 307,000 Pa, leading to a total of approximately 7.6 x 1023 molecules, compared to the incorrect calculation of 5.12 x 1023 molecules using gauge pressure alone.

PREREQUISITES
  • Understanding of the Ideal Gas Law
  • Knowledge of gauge pressure vs. absolute pressure
  • Familiarity with the constants: Boltzmann's constant (kb)
  • Basic skills in unit conversion (psi to Pa)
NEXT STEPS
  • Learn about the Ideal Gas Law and its applications
  • Study the differences between gauge pressure and absolute pressure
  • Explore the significance of Boltzmann's constant in thermodynamics
  • Practice converting pressure units from psi to Pascals
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Students in physics or engineering courses, particularly those studying thermodynamics and gas laws, as well as educators explaining pressure concepts in practical applications.

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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??
 
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SmugBug said:
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.
 
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30 psi is the gauge pressure. A gauge under atmospheric pressure reads zero.

Edit: oops haruspex said it first
 
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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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