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16 December, 09:32

the air in a tire is initially at 380 kpa, 20 C, when the tire volume is 0.120 m^3. as the tire is warmed by the sun, the pressure becomes 450 kpa and the tire volume increases by 5%. determine the final temperature and the mass of air in the tire.

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  1. 16 December, 09:46
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    final temperature is 364.32 K

    mass of air is 0.5423 kg

    Explanation:

    given data

    pressure p1 = 380 kPa

    volume v1 = 0.120 m³

    temperature = 20°C = 20 + 273 = 293 K

    pressure p2 = 3450 kPa

    volume v2 = 5% increase

    to find out

    final temperature and the mass

    solution

    we consider here ideal gas

    so equation is

    p1v1 / t1 = p2v2/t2

    put here all value and find t2

    and v2 is = 0.120 (1 + 0.05) = 0.126 m³

    so

    t2 = p2v2 / p1v1 * t1

    t2 = (450 * 0.126) / (380 * 0.120) * 293

    t2 = 364.32 K

    so final temperature is 364.32 K

    and

    mass = p2v2 / Rt2

    here R gas constant is 0.287 kJ/kg. K

    so

    mass = (450 * 0.126) / (0.287 * 364.32)

    mass = 0.5423

    so mass of air is 0.5423 kg
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