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Thermo: Compressor-flowing system analysis

  1. Oct 9, 2011 #1
    Thermo: Compressor--flowing system analysis

    1. The problem statement, all variables and given/known data

    A compressor takes 90 kg/min of helium at 120 kPa and 310 K and compresses it to
    700 kPa and 430K. A heat loss of 20 kJ/kg of helium flowing is noted.

    Determine:

    (a) the work required by the compressor (kJ/kg), and
    (b) the power required to drive the air compressor (kW).
    Assume helium is an Ideal Gas; M = 4 kg/kmol; Cp = 5/2R.



    2. Relevant equations

    PLEASE SEE ATTACHED PHOTO FOR MY WORK AND ATTEMPT.

    3. The attempt at a solution

    The solutions are given as
    (a) 643.6 kJ/kg
    (b) +965.4 kW

    My questions are:

    a) I would not have realized that this 643.6 kJ/kg result was actually what was asked (work req'd by compressor) had the solution not been given. This was just an intermediate result to what I thought I was working towards. So how would I know that "the work req'd by compressor" is actually asking for this? And what symbol would this be denoted by?

    Work (W) has SI units of J = Nm = kgm^2/s^2. So it's not W... but what? The phrasing of the question has me confused.

    b) According my Mass Energy balance expression of the 1st LoTh; with cancellations and strategic assumptions, Wdot= mdot(deltah) -Qdot.

    So to calculate Wdot, I have a unit mismatch unless I bring Qdot inside the parenthetical expression. But multiplying Qdot by mdot is nowhere in my relation of the 1st Law. This seems like magic--and bad mathematics--to me. But it yields the correct (given) solution. Some insight here would be helpful.

    Thanks!
    JC
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
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