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Thermodynamics Question and My Answer

  1. Mar 6, 2008 #1
    [SOLVED] Thermodynamics Question and My Answer

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

    During a cloudy day of the summer season, a driver inflates his car tyres (max allowed pressure is 44PSI(Gauge)) to 38PSI(Gauge) at a petrol station. the temperature of the air inside one of the tires is [tex]77^oF[/tex] and volume of the tire is [tex]1ft^3[/tex]. Later, the sun comes out and the air inside the tire experience a temperature rise of [tex]36^oF[/tex]. Assuming the volume to be constant determine whether the tire will burst or not.

    2. Relevant equations

    P(Absolute) = P(Ambient) + P (Gauge)
    Conversion from F to R
    Conversion from PSI to [tex]\frac{lbf}{ft^2}[/tex]

    3. The attempt at a solution

    First did the relevant conversions.

    Then used :-

    [tex]P_{1}v = RT_{1}[/tex]

    [tex]P_{2}v = RT_{2}[/tex]

    Where [tex]R[/tex] = Individual Gas Constant

    Where [tex]v[/tex] = Specific Volume

    Took the ratios, because the volume remains constant and so does the value of R :-

    [tex] \frac{P_{1}}{P_{2}} = \frac{T_{1}}{T_{2}}[/tex]

    Made relevant calculations and then did reverse conversions. Got the answer to be 41.54 PSI (Gauge). Which indicates that tire doesn't bursts. Is this the correct answer ?
    Last edited: Mar 6, 2008
  2. jcsd
  3. Mar 6, 2008 #2


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