Pressure in a tire

  1. 1. The problem statement, all variables and given/known data

    An automobile tire has a volume of 1.50x10^-2 m^3 on a cold day when the temperature of the air in the tire is 3.0 C and atmospheric pressure is 1.02 atm. Under these conditions the gauge pressure is measured to be 1.65 atm. After the car is driven on the highway for 30 min, the temperature of the air in the tires has risen to 47.0 C and the volume has risen to 1.65x10^-2 m^3.

    What then is the gauge pressure?

    T1 = 276 K
    V1 = 1.50 * 10^-2
    p1 = 1.65

    T2 = 320 K
    V2 = 1.65 * 10^-2



    2. Relevant equations

    p1V1/T1 = p2V2/T2

    3. The attempt at a solution

    p2 = p1 * V1/V2 * T2/T1

    p2 = 1.65 * (1.50 * 10^-2)/(1.65 * 10^-2) * 320/276

    p2 = 1.74

    The answer only needs to be to three significant digits. This answer is close to the correct answer, but it's still not correct. I know that somehow the atmospheric pressure of 1.02 atm is significant, but I can't figure out what to do with it.
     
  2. jcsd
  3. The gauge pressure is the net pressure acting on the tyre. I think the pressure that must be used in the equation is actually the gross pressure in the tyre, e.g., p_1+p_a.

    Does this give a better answer?
     
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