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8 April, 15:31

When they say in the United States that a car's tire is filled "to 32 lb," they mean that

its internal pressure is 32 lbf/in² above the ambient atmosphere. If the tire is at sea level,

has a volume of 3.0 ft³, and is at 75°F. Estimate the total weight of air, in lbf, inside the tire

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  1. 8 April, 18:40
    0
    0.71 lbf

    Explanation:

    Use ideal gas law:

    PV = nRT

    where P is absolute pressure,

    V is volume,

    n is number of moles,

    R is universal gas constant,

    and T is absolute temperature.

    The absolute pressure is the sum of the atmospheric pressure and the gauge pressure.

    P = 32 lbf/in² + 14.7 lbf/in²

    P = 46.7 lbf/in²

    Absolute temperature is in Kelvin or Rankine:

    T = 75 + 459.67 R

    T = 534.67 R

    Given V = 3.0 ft³, and R = 10.731 ft³ psi / R / lb-mol:

    PV = nRT

    (46.7 lbf/in²) (3.0 ft³) = n (10.731 ft³ psi / R / lb-mol) (534.67 R)

    n = 0.02442 lb-mol

    The molar mass of air is 29 lbm/lb-mol, so the mass is:

    m = (0.02442 lb-mol) (29 lbm/lb-mol)

    m = 0.708 lbm

    The weight of 1 lbm is lbf.

    W = 0.708 lbf

    Rounded to two significant figures, the weight of the air is 0.71 lbf.
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