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Tire pressure - physics?
A tire contain 1 cubic foot of air at gauge pressure of 28 lb/in2. How much additonal air at atmospheric pressure must be pumped into the tire to raise the pressure to 36 lb/in2 at the same temperature?
Please show your work.
1 Answer
- Anonymous2 years agoFavorite Answer
Atmospheric pressure = 15 psi. We start with a volume of 1ft³ at with air at an *absolute* pressure of (28+15=) 43psi and want to add air in order to raise the *absolute* pressure to (36+15=) 51psi.
The ideal gas equation is PV = nRT. Rearranged this gives n = PV/(RT).
(amount of air initially in tire) + (amount of additional air from atmosphere) = (final amount of air in tire)
Since T is constant, this gives:
P₁V₁/(RT) + P₂V₂/(RT) = P₃V₃/(RT)
RT cancels. V₁ = V₃ (= 1ft³). We want to find V₂.
P₁V₁ + P₂V₂ = P₃V₃
43*1 + 15*V₂ = 51*1
V₂ = (51-43)/15 = 0.53 ft³ to 2 sig. figs.