Question

when the temperature of an automobile tire is 20 degrees c, the pressure in the tire reads 29 psi on a tire gauge. (the gauge measures the difference between the pressures inside and outside the tire.) what is rhe pressure when the tire heats up to 39 degrees c while driving? you may assume that the volume of the tire remains the same and that the atomspheric pressure is a steady 14 psi.

Answer 1

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volume is constant (because the tyre has a virtually fixed volume).

Then using,
P₁/T₁ = P₂/T₂

Because the gauge measures the pressure difference, the initial actual pressure inside the tyre is:
P₁ = 14 + 29 = 43 psi

Initial temperature: T₁ = 273 + 20 = 293K (must use absolute temperatures for the formula)
Final temperature: T₂ = 273 + 39 = 312K

43/293 = P₂/312
P₂ = 45.788 psi

(The gauge would read 45.788 - 14 = 31.788 psi)

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