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12 June, 06:24

0. One kg of methane is contained in a piston/cylinder device at 0.8 MPa and 250°C. It undergoes a reversible isothermal expansion to 0.3 MPa. Methane can be considered an ideal gas under these conditions. How much heat is transferred?

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  1. 12 June, 07:13
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    234.57 kJ of heat is transferred.

    Explanation:

    Q = ∆U + W

    W (work done) = nRTln (P1/P2)

    n is number of moles of methane = mass/MW = 1/16 = 0.0625 kg mol.

    R is gas constant = 8.314 kJ/kg mol. K

    T is temperature = 250°C = 250 + 273 = 523 K

    P1 = 0.8 MPa

    P2 = 0.3 MPa

    W = 0.0625*8.314*523*ln (0.8/0.3) = 267.57 kJ

    From steam table

    At 0.8 MPa (8*10^5 Pa = 8bar), initial specific internal energy = 2577 kJ/kg

    At 0.3 MPa (3*10^5 Pa = 3 bar), final specific internal energy = 2544 kJ/kg

    Change in specific internal energy = 2544 - 2577 = - 33 kJ/kg

    ∆U (change in internal energy) = change in specific internal energy * mass = - 33 kJ/kg * 1 kg = - 33 kJ

    Q (Quantity of heat transferred) = - 33 kJ + 267.57 kJ = 234.57 kJ
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