Ideal Gas Law Application: Finding the Temperature of Air in a Tire

[iflabs]

[SOLVED] Ideal Gas Law Application

Homework Statement

One Sunday morning a family takes an automobile trip to Grandma's. At the start of the trip, the temperature is 288K (15C), and the gauge pressure in the tires is 32lb/in^2 (psi). (The gauge pressure is the excess over 14.5 psi, the exterior air pressure.) After an hour's ride over an interstate highway, the gauge pressure in the tires is 38 psi. What is the temperature of the air in the tires, assuming that air behaves as an ideal gas? Neglect any changes in volume of the tires.

Homework Equations

PV=nRT

The Attempt at a Solution

3. After working around with the universal gas law, the forumla I used is: T2=(P2*T1)/P1

T2=(38/32)*288=342K

342-273=69C

The textbook gives the answer 52C. What am I doing wrong? Did I use the wrong units?

 

[Dick]

They already told you. Gauge pressure is pressure above 14.5 psi. Try solving T2=(38+14.5)*T1/(32+14.5).

 

[iflabs]

They already told you. Gauge pressure is pressure above 14.5 psi. Try solving T2=(38+14.5)*T1/(32+14.5).

Hmmm, I missed that part. What does it mean when the gauge pressure is above 14.5psi?

I forgot, but why can't you use the celsius scale to do the problem?

 

[Dick]

What they meant is that real pressure=14.5psi+gauge pressure. It's the pressure you would read with a tire gauge, for example. If it reads 0psi that just means that the pressure in the tire is the same as atmospheric pressure. You can't use degrees C because 0C=273K, 1C=274K, but 274/273 is NOT equal to 1/0. You tell me what went wrong.