How many air molecules are there inside the tire?

[SmugBug]

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??

 

[haruspex]

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.

 

[Nathanael]

30 psi is the gauge pressure. A gauge under atmospheric pressure reads zero.

Edit: oops haruspex said it first

 

[Chestermiller]

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.