Before beginning a long trip on a hot day, a driver inflates anautomobile tire t

Question

Before beginning a long trip on a hot day, a driver inflates anautomobile tire to a gauge pressure of 2.30 atm at 300 K. At the end of the trip the gaugepressure has increased to 2.80 atm. (a) Assuming that the volume has remainedconstant, what is the temperature of the air inside the tire?
1 K
(b) What percentage of the original mass of air in the tire shouldbe released so the pressure returns to the original value? Assumethe temperature remains at the value found in (a), and the volumeof the tire remains constant as air is released.
2% (a) Assuming that the volume has remainedconstant, what is the temperature of the air inside the tire?
1 K
(b) What percentage of the original mass of air in the tire shouldbe released so the pressure returns to the original value? Assumethe temperature remains at the value found in (a), and the volumeof the tire remains constant as air is released.
2%

Explanation / Answer

(a) Assuming that the volume has remained constant, what is thetemperature of the air inside the tire?
     {New Temp} = {OldTemp}*{New Absolute Pressure}/{Old AbsolutePressure} =
          = (300degK)*(1.0 + 3.20 abs atm)/(1.0 + 2.70 absatm)
          = 341 degK

(b) Whatpercentage of the original mass of air in the tire should bereleased so the pressure returns to
the original value? Assume the temperature remains at the valuefound in (a), and the volume of the
tire remains constant as air is released.
      {New"n"}/{Orig "n"} =
          = {Orig Pressure}/{High Pressure AfterDriving}
   = (1.0 + 2.70 absatm)/(1.0 + 3.20 abs atm)
          = 0.881
----> {% Mass Released}= (100)*(1.0 -(0.881)) = 11.9 %
       
.

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