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

Question

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.    

Answer 1

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

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

                                                  =14.7+31 = 45.7 lb/in²

Initial temperature, T₁ = 52^oF = 512 R

Final temperature, T₂ =102^oF = 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- P_atm

          _{= 50.163-14.7}

          = 35.463 lb/in²

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

Comments

What is the "R" temperature that you converted to?

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R is the temp units in rankine.

Convert Fahrenheit to rankine to add 460