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27 January, 14:05

8. Air at 25C, 100 kPa and air at 50C, 200 kPa at 1 to 1 volume ratio are mixed inside an adiabatic compressor to 55C, 500 kPa and pushed through an isothermal nozzle with inlet area a quarter the size of the outlet area and reaching 10 m/s at 300 kPa. How much work is required if we want to get 5 kg of this mixture

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  1. 27 January, 14:29
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    Workdone, w = 68.935 kJ

    Explanation:

    m1h1 + m2h2 + Q = m3h3 - Wc

    Final mass of mixture,

    m3 = m1 + m2 = 5kg

    p1V1 = m1R1T1

    p2V2 = m2R2T2

    Since they are at 1:1,

    V1 = V2 and R1 = R2

    Comparing equations,

    p1/p2 = (m1/m2) x (T1/T2)

    m1/m2 = (100/200) x ((50 + 273) / (25+273))

    m1/m2 = 0.542

    m1 = 0.542m2

    m3 = m1 + m2

    5 = m2 + 0.542m2

    m2 = 3.243kg

    m1 = 1.757 kg

    Workdone is given as,

    Wc = m3h3 - m1h1 - m2h2

    h = Cp x T, since air is an ideal gas

    Cp = 1.005kJ/kGK

    Wc = (5 x 1.005 x (55+273)) - (1.757 x 1.005 x 298) - (3.243 x 1.005 x 323)

    Wc = 68.935 kJ
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