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castrodisastro

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## Homework Statement

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?

## Homework Equations

Gay-Lussac's Law

*p*_{1}/T_{1}=*p*_{2}/T_{2}## The Attempt at a Solution

Part a)

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.

**T**

T

_{1}= 26.1 °F = 269.9 KT

_{2}= 79.1 °F = 299.31 K

*p*_{1}=33.5 psi = 230974.3692 Pa ≈ 231 kPaSolving Gay-Lussac's Law to solve for the final pressure...

*p*_{1}T_{2}/T_{1}=*p*_{2}Finally

**(230974.3692 Pa)(299.31K)/(269.9K)=**

*p*_{2}=256142.7879Pa ≈ 256 kPaPart b)

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.

Thanks