A car tire has the following dimensions: outer diameter 21 inches, inner diamete

Question

A car tire has the following dimensions: outer diameter 21 inches, inner diameter 15 inches, width 6 inches, which is volume of 2.3562ft3

a) The tire has been inflated to 28 psig. This is done when the tire is cold, so the temperature is 45°F. Recalling that the molecular weight of air is 29, determine the mass of the air inside the tire in lbm.

b) If the tire is driven for a while, it will heat up to 120°F. Due to the fact that materials expand when they are hotter, the volume of the tire also increases slightly, by 3%. Of course the mass cannot change since no new air was added. What is the new gauge tire pressure?

Explanation / Answer

a) Volume of tire = pi (21^2 - 15^2) x 6

V = 4071.504 inch^3

inch = 0.0833 m

V = 4071.504 x 0.08333^3 m^3 = 2.36 ft^3

b) P = 28 psig = 28 x 6894.76 pa = 193053 Pa

V = 2.36 ft^3 = 0.0668 m^3

T = 45 deg F = 280.4 K

using PV = n RT

193053 x 0.0688 = n x 8.314 x 280.4

n = 5.53 mol

mass of gas = 5.53 x 29 = 160.4 g .........Ans

c) V = 1.03 x 0.0668 = 0.0687 m^3

T = 120 deg F = 322 K

n = 5.53

PV = n RT

P (0.0687) = 5.53 x 8.314 x 322

P = 215425.83 Pa

P (in psig) = 31.24 psig

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