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1 April, 07:08

Saturated water vapor at 200 kPa is condensed into a saturated liquid via a constant-pressure process inside of a piston-cylinder device. To complete this process, heat is removed from the system and transferred to the environment which is at a constant temperature of 90C. Is this process possible?

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  1. 1 April, 07:40
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    The process is not possible

    Explanation:

    if we want to determine if the process is possible, we can check with the second law of thermodynamics

    ΔS≥ ∫dQ/T

    for a constant temperature process (condensation)

    ΔS≥ 1/T ∫dQ

    and from the first law of thermodynamics

    ΔH = Q - ∫VdP, but P=constant → dP=0 → ∫VdP=0

    Q=ΔH

    then

    ΔS≥ΔH/T

    from steam tables

    at P = constant = 200 Kpa → T = 120°C = 393 K

    at P = constant → H vapor = 2201.5 kJ/kg, H liquid = 1.5302 kJ/kg

    , S vapor = 7.1269 kJ/kg, S liquid 1.7022 kJ/kg

    therefore

    ΔH = H vapor - H liquid = 2201.5 kJ/kg - 1.5302 kJ/kg = 2199.9698 kJ/kg

    ΔS = S vapor - S liquid = 7.1269 kJ/kg - 1.7022 kJ/kg = 5.4247 kJ/kg

    therefore since

    ΔS required = ΔH/T = 2199.9698 kJ/kg / (393 K) = 5.597 kJ/kg K

    and

    ΔS = 5.4247 kJ/kg ≤ ΔS required=5.597 kJ/kg K

    the process is not possible
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