An engine operates on a Carnot cycle that uses 1mole of an ideal gas as the working substance and operates from a most compressed stage

Question

An engine operates on a Carnot cycle that uses 1mole of an ideal gas as the
working substance and operates from a most compressed stage of 100 Nm and
327 K. It expands isothermally to a pressure of 90 Nm and then adiabatically to a
most expanded stage of 27 K. Calculate the AU, 9, and w for each step. Calculate
the net work done and the efficiency of the cycle [Cv,m for the gas) is 25 J/k/mol.​

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Yến Oanh 6 months 2021-07-29T23:50:34+00:00 1 Answers 6 views 0

Answers ( )

    0
    2021-07-29T23:52:18+00:00

    Answer:

    Step 1;

    q = w = -0.52571 kJ, ΔS = 0.876 J/K

    Step 2

    q = 0, w = ΔU = -7.5 kJ, ΔH = -5.00574 kJ

    Explanation:

    The given parameters are;

    P_i = 100 N·m

    T_i = 327 K

    P_f = 90 N·m

    Step 1

    For isothermal expansion, we have;

    ΔU = ΔH = 0

    w = n·R·T·ln(P_f/P_i) = 1 × 8.314 × 600.15 × ln(90/100) = -525.71

    w ≈ -0.52571 kJ

    At state 1, q = w = -0.52571 kJ

    ΔS = -n·R·ln(P_f/P_i) = -1 × 8.314 × ln(90/100) ≈ 0.876

    ΔS ≈ 0.876 J/K

    Step 2

    q = 0 for adiabatic process

    ΔU = 25×(27 – 327) = -7,500

    w = ΔU = -7.5 kJ

    ΔH = ΔU + n·R·ΔT

    ΔH = -7,500 + 8.3142 × 300 = -5,005.74

    ΔH = ΔU = -5.00574 kJ

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