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Car Tire Pressure

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

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

    3. 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?
     
  2. jcsd
  3. Jun 16, 2009 #2

    LowlyPion

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    Well, what is the ratio of the temps in Kelvin?
     
  4. Jun 16, 2009 #3
    The ratio of T1/T2 = (257 K)/(317.2 K) = 0.8102143758
     
  5. Jun 16, 2009 #4

    LowlyPion

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    So what would you do with that? Multiply or divide into the 57.2?
     
  6. Jun 16, 2009 #5
    I'm assuming multiply:

    So, 57.2 psi X 0.8102143758 = 46.3 psi BUT THIS IS NOT THE RIGHT ANSWER!
     
  7. Jun 16, 2009 #6

    LowlyPion

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    Why would you assume the pressure would get smaller if the temperature increased?
     
  8. Jun 16, 2009 #7
    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.
     
  9. Jun 16, 2009 #8

    LowlyPion

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    But 70.6 is not gauge pressure is it?
     
  10. Jun 16, 2009 #9
    Oh...I got it. Thank you!
     
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