# Ideal Gas Law Car TIre Problem

1. Jan 16, 2006

### atelaphobia

here's another one that stumped me

An automobile tire is inflated with air originally at 10C and normal atmospheric pressure. During the process the air is compressed to 28% of its original volume and the temperature is increased to 40C.
a) what is the tire pressure?
b) after the car is driven at high speed the tire air temperature rises to 85C and the interior volume of the tire increases by 2%. what is the new tire pressure (absolute) in pascals?

the only reason why i dont know how to start this problem is because i dont know what is the initial pressure. all it says is "normal atmospheric pressure"

2. Jan 16, 2006

### atelaphobia

ok i got the first part
a)

Pinitial/T initial=Pfinal/Tfinal

normal pressure= 1atm= 101.325kPa
convert temps into Kelvins
T initial= 283.15
Tfinal= 313.15

SO...

101.325/283.15=P(.28)/313.15

P= 400kPa

but now i dont know how to get the second one
I know the answer for b is 449 kPa

Last edited: Jan 16, 2006
3. Jan 16, 2006

### atelaphobia

i think i solved the second part but tell me if this makes sense at all!

the temp rises to 85C (359.15 K) and tire increases volume by 2%

so using the numbers from part A with the same equation

400/313.15=P/358.15
solve for P=457.726 BUT it's saying the volume of the tire increased by 2%
so... 2% of 457.726 is 9.154

since we gotta incorporate the 2% factor i subtracted 457.726-9.154
gave me 448.57 which is 449kPa

now did i do that right??