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6 August, 07:54

During an expansion process, the pressure of a gas changes from 15 to 140 psia according to the relation P = aV + b, where a = 5 psia/ft3 and b is a constant. If the initial volume of the gas is 7 ft3, calculate the work done during the process.

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  1. 6 August, 09:59
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    The work done during the process is 359 btu

    Explanation:

    Given-

    P1 = 15psia

    P2 = 140 psia

    V1 = 7ft³

    a = 5 psia/ft³

    b = C

    P = aV + b

    Work done, W = ?

    P1 = aV1 + b

    15 = 5 (7) + b

    b = - 20 psia

    P2 = aV2 + b

    140 = 5 (V2) - 20

    V2 = 32 ft³

    The work done by the process is the area under the curve which is trapezoidal.

    Therefore,

    Work done, W = area of trapezoid

    = (P2 + P1 / 2) (V2 - V1)

    = (140 + 15 / 2) (32 - 7)

    = 1937.5 psia ft³

    = 1937.5 / 5.4039 = 359 btu

    Therefore, the work done during the process is 359 btu
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