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27 January, 15:38

An automobile tire with a volume of 0.8 m3 is inflated to a gage pressure of 200 kPa. Calculate the mass of air in the tire if the temperature is 23 °C.

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  1. 27 January, 15:48
    0
    2.83 kg

    Explanation:

    Given:

    Volume, V = 0.8 m³

    gage pressure, P = 200 kPa

    Absolute pressure = gage pressure + Atmospheric pressure

    = 200 + 101 = 301 kPa = 301 * 10³ N/m²

    Temperature, T = 23° C = 23 + 273 = 296 K

    Now,

    From the ideal gas equation

    PV = mRT

    Where,

    m is the mass

    R is the ideal gas constant = 287 J/Kg K. (for air)

    thus,

    301 * 10³ * 0.8 = m * 287 * 296

    or

    m = 2.83 kg
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