I put air in the tires of my car during the summer, while it was 34.9˚C outside (about 94.82˚F). My tires say to fill them to a pressure of 203,000 Pa. Boltzmann's constant is 1.38 x 10-23 J/KA) If my tires have a volume of 0.0100 m3, how many air molecules are in the tire?B) These tires go all summer without losing any air, however come fall the temperature drops down to 2.04˚C (about 35.672˚F). Assuming the volume doesn’t change (because it doesn’t) what is the new pressure in my tires?

Answered: I put air in the tires of my car during…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

I put air in the tires of my car during the summer, while it was 34.9˚C outside (about 94.82˚F). My tires say to fill them to a pressure of 203,000 Pa.

Boltzmann's constant is 1.38 x 10^-23 J/K

A) If my tires have a volume of 0.0100 m³, how many air molecules are in the tire?

B) These tires go all summer without losing any air, however come fall the temperature drops down to 2.04˚C (about 35.672˚F). Assuming the volume doesn’t change (because it doesn’t) what is the new pressure in my tires?

Expert Solution

Step 1

From the ideal gas law, pressure, temperature and volume of a gas are related as

$P V = n R T P i s p r e s s u r e V i s v o l u m e T i s t e m p e r a t u r e n i s n u m b e r o f m o l e s o f t h e g a s R i s t h e u n i v e r s a l g a s c o n s \tan t$