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 32 psi while the outside temperature is 26 °F and then make sure your valve caps are airtight. You arrive in Florida two days later, and the temperature outside is a pleasant 69 °F.

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

(b) If you let air out of the tires to bring the pressure back to the recommended 32, what percentage of the original mass of air in the tires will you release?

Explanation / Answer

a). p,t,v and n denote the pressure ,temperature,volume
and number of moles.      1 &2 denote the initial and final conditions.

clearly the volume of the air will remain constant.pressure has been converted to atm and temperature to kelvin.

hence,
p1/t1=p2/t2
2.177/269.67 = p2/293.55

p2=2.37atm=2.37*105N/m2=237kPa

b)in this case we want to have the pressure constant,volume available to air in tyre remains constant but number of moles change upon releasing air.

n1*t1=n2*t2

n1-n2/n1=t2-t1/t1=fraction of air released

=293.55-269.67/269.67=0.088

percentage of air released=0.088*100=8.8%

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