# Car Tire Pressure

## Homework Statement

A car tire gauge is used to fill a tire to a gauge pressure of 42.5 lb/in2 on a cold morning when the temperature is -16 C. Atmospheric pressure is 14.7 lb/in2 and 0 C = 273 K.

What would the tire gauge read when the tire has been heated up to 44.2 C?

## Homework Equations

P2 = P1 (atmospheric pressure) + ϱgh (gauge pressure)
PV= nRT
P1/T1 = P2/T2

## The Attempt at a Solution

P2 = (14.7 lb/in2 + 42.5 lb/in2) = 57.2 lb/in2

I don't really know if this is even the right first step. I just recognized that gauge pressure is ϱgh. What should I do next?

LowlyPion
Homework Helper
Well, what is the ratio of the temps in Kelvin?

The ratio of T1/T2 = (257 K)/(317.2 K) = 0.8102143758

LowlyPion
Homework Helper
The ratio of T1/T2 = (257 K)/(317.2 K) = 0.8102143758

So what would you do with that? Multiply or divide into the 57.2?

I'm assuming multiply:

So, 57.2 psi X 0.8102143758 = 46.3 psi BUT THIS IS NOT THE RIGHT ANSWER!

LowlyPion
Homework Helper
I'm assuming multiply:

So, 57.2 psi X 0.8102143758 = 46.3 psi BUT THIS IS NOT THE RIGHT ANSWER!

Why would you assume the pressure would get smaller if the temperature increased?

If you divide:

57.2 psi/0.81 = 70.6 psi ALSO NOT THE RIGHT ANSWER!

The right answer is 55.8986 psi, so the pressure does get smaller.

LowlyPion
Homework Helper
If you divide:

57.2 psi/0.81 = 70.6 psi ALSO NOT THE RIGHT ANSWER!

The right answer is 55.8986 psi, so the pressure does get smaller.

But 70.6 is not gauge pressure is it?

Oh...I got it. Thank you!