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 33.5 psi while the outside temperature is 26.1 °F and then make sure your valve caps are airtight. You arrive in Florida two days later, and the temperature outside is a pleasant 79.1 °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 33.5 psi, what percentage of the original mass of air in the tires will be released?
Gay-Lussac's Law p1/T1=p2/T2
The Attempt at a Solution
The rubber tire keeps the volume constant while varying the pressure within depending on the temperature. From this information, I deduced that I needed to use Gay-Lussac's Law to determine the new pressure.
First I converted everything to SI units.
T1 = 26.1 °F = 269.9 K
T2 = 79.1 °F = 299.31 K
p1=33.5 psi = 230974.3692 Pa ≈ 231 kPa
Solving Gay-Lussac's Law to solve for the final pressure...
(230974.3692 Pa)(299.31K)/(269.9K)=p2=256142.7879Pa ≈ 256 kPa
If we let out (256,142.7879Pa - 230,974.3692Pa =) 25,168.4187Pa to bring the pressure back to what we started, then releasing 25,168.4187 Pa of pressure decreases the tires mass by some percentage x.
Since Increasing the pressure to 256,142.7879 Pa doesn't change the mass of the air inside until we let some out, we can consider the percentage change in the pressure
[(25,168.4187 Pa)/(256,142.7879 Pa)]*100%=9.826%
9.826% of mass of air has been released.
My homework is an online assignment with 11 questions. I can submit each of my answers in two fields, one containing the numeric value, and the other contains the units(unless given to me). I can submit my answer and it will tell me if I am correct or incorrect.
I got part b correct but not part a. I tried expressing the pressure in Pascals, kiloPascals, and psi (just to check), and I tried using the exact value(calculator's limit), and 3 significant figures, I tried expressing in scientific notation, but it still says I'm incorrect. Is it not looking for the value that I found as the new pressure? I got part b correct so I would assume my answer to part a is correct also.
Any help(or insight on ideal gases in general) is appreciated.