Before embarking on a car trip from Michigan to Florida to escape the winter col

Question

Before embarking on a car trip from Michigan to Florida to escape the winter cold, you inflate the tires of your car to a manufacturer-suggested pressure of 31 psi while the outside temperature is 27 °F and then make sure your valve caps are airtight. You arrive in Florida two days later, and the temperature outside is a pleasant 72 °F.

(a) What is the new pressure in your tires, in SI units?

(b) If you let air out of the tires to bring the pressure back to the recommended 31, what percentage of the original mass of air in the tires will you release?

Please and thank you. Feel free to write as much because I would like to learn how to work this type of problem.

Explanation / Answer

let,

initial pressure is p1=31psi

p1=213737.467 Pascal

=213.737 KPascal

initial tempereature is T1=27 oF =270.37 K

now,

final temperature T2=72 oF =294.26 K

a)

let, final pressure is p2

by using Charles's law,

p1/T1=P2/T2

===>

p2=p1*(T2/T1)

=213737.467*(294.26/270.37)

=232623.394 pascal

=232.623 Kpascal

b)

p1/p2=(m1*T1)/(m2*T2)

====> p1=P2

(m1*T1)=(m2*T2)

m2=(T1/T2)*m1

= (270.37/294.26))*m1

m2=0.92 m1

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