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An automobile tire is filled with air to a gauge pressure of 31 lb/in^2 at 52 degrees F. ?

0 votes

Update : After driving for several hours, the temperature of the tire reaches 102 degrees F. Assume the volume doesn't change appreciably. What is the tire gauge read at this temperature? Assume the air outside the tire is at atmospheric pressure 14.7 lb/in^2. Answer in units of lb/in^2.    

asked Jul 23, 2014 in PHYSICS by anonymous

1 Answer

0 votes

Initial gauge pressure, (P₁)g= 31 lb/in2 

Initial actual pressure,(P₁) = Patm +(P₁)g

                                                  =14.7+31 = 45.7 lb/in2

Initial temperature, T₁ = 52oF = 512 R

Final temperature, T₂ =102oF = 562 R

Calculate the final actual pressure by using the Charle's law

P₁/T₁ =P₂/T₂

45.7/512 = P₂/562

P₂ = 50.163 lb/in2

Calculate the actual gauge pressure:

(P₂)g = P₂- Patm

          = 50.163-14.7

          = 35.463 lb/in2

Therefore , the gauge pressure at 102oF is 35.463 lb/in2

answered Jul 23, 2014 by bradely Mentor
edited Jul 26, 2014 by bradely
What is the "R" temperature that you converted to?

R is the temp units in rankine.

Convert Fahrenheit to rankine to add 460

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