# How many air molecules are there inside the tire?

## 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?

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

( 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
Homework Helper
Gold Member
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.

• SmugBug
Nathanael
Homework Helper
30 psi is the gauge pressure. A gauge under atmospheric pressure reads zero.

Edit: oops haruspex said it first

• SmugBug
Chestermiller
Mentor
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.