Tire Pressure Gauge Reading at 44.2°C

[PrideofPhilly]

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]

Well, what is the ratio of the temps in Kelvin?

 

[PrideofPhilly]

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

 

[LowlyPion]

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?

 

[PrideofPhilly]

I'm assuming multiply:

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

 

[LowlyPion]

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?

 

[PrideofPhilly]

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]

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?

 

[PrideofPhilly]

Oh...I got it. Thank you!