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14 March, 14:13

Ammonia, 2 kg, at 400 kPa, 40'C is in a piston/cylinder together with an unknorvn mass of sat-urated liquid ammonia at 400 kPa. The pistonis loaded, so it maintains constant pressure, andthe two masses are allowed to mix to a final uni-form state ofsaturated vapor u'ithout external heattransfer. Find the total exergy destruction in theprocess.

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  1. 14 March, 15:39
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    Given the following information

    Initial Pressure P1 = 400kPa

    Initial temperature T1 = 40°C

    Mass m = 2kg

    T (ambient) Ta = 298k

    From superheated Ammonia table, corresponding to P1 = 400kPa and T1 = 40°C, we can find the first stage entropy and enthalpy

    h1 = 1543.6 KJ/Kg

    s1 = 5.7111 KJ/KgK

    Using interpolation method to find the second stage enthalpy and entropy

    From saturated ammonia table,

    at P = 354.9KPa, the liquid specific entropy and enthalpy is.

    sf = 0.6266 KJ/KgK

    hf = 157.31 KJ/Kg

    Also, From saturated ammonia table, at P' = 429.6KPa, the liquid specific entropy and enthalpy is.

    sf' = 0.7114 KJ/KgK

    hf' = 180.36 KJ/Kg

    So, using interpolation, stage 2 specific enthalpy and entropy is

    s2 = sf + (P1 - P) / (P' - P) * (sf' - sf)

    s2 = 0.6266 + (400-354.9) / (429.6-354.9) * (0.7114-0.6266)

    s2 = 0.6266 + (45.1 / 74.7) * 0.0848

    s2 = 0.6266 + 0.0512

    s2 = 0.6778 KJ/KgK

    h2 = hf + (P1 - P) / (P' - P) * (hf' - hf)

    h2 = 157.31 + (400-354.9) / (429.6-354.9) * (180.36-157.31)

    h2 = 157.31 + (45.1 / 74.7) * 23.05

    h2 = 157.31 + 13.916

    h2 = 171.23 KJ/Kg

    At superheated ammonia table corresponding to P3 = 400Kpa, we can find the final stage specific entropy and enthalpy

    s3 = 5.3559 KJ/KgK

    h3 = 1440.2 KJ/Kg

    Using equation of continuity

    m1 + m2 = m3

    We can now calculate the stage two mass

    m1•h1 + m2•h2 = (m1+m2) •h3

    Make m2 subject of the formula

    m2•h2 - m2•h3 = m1•h3 - m1•h1

    m2 (h2 - h3) = m1 (h3 - h1)

    m2 = m1• (h3 - h1) / (h2 - h3)

    m2 = 2 * (1440.2 - 1543.6) / (171.23 - 1440.2)

    m2 = 2 * - 103.4 / - 1268.97

    m2 = 0.163 kg

    Then, the final mass is equal to

    m3 = m1 + m2

    m3 = 2 + 0.163

    m3 = 2.163 kg

    Calculating the irreversible process

    I = Ta (m3•s3 - m2•s2 - m1•s1)

    I = 298 (2.163 * 5.3559 - 0.163 * 0.6778 - 2 * 5.7111

    I = 298 (11.5848 - 0.1105 - 11.4222)

    I = 298 * 0.0521

    I = 15.5258 KJ

    I ≈ 15.53 KJ
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