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Thermodynamics question

  1. Jan 2, 2007 #1
    1. The problem statement, all variables and given/known data

    A river of mean width 400m and depth 4m flows at a mean velocity of 0.3m/s. The river is used as a sink by 10 power stations each of 2000MW output. The heat loss from the river to the atmosphere between the first and last power stations amounts to 10,000 MW. Determine the rise in river temperature as it flows past the 10 power stations. Take the value of Cp as 4.18 kJ/kgK and assume the power stations operate at half the maximum possible efficiency appropriate to source and sink temperatures of 1200K and 310K respectively.

    3. The attempt at a solution

    So far I've only been able to work out the mass flow rate, the thermal efficiency and the maximum power output of the 10 stations:

    m.f.r= density x area x velocity
    = 1000 x 1600 x 0.3 = 480000kg/s

    max. efficiency = (Th-Tl)/Th = (1200-310)/1200 = 0.74
    actual efficiency = 0.74/2 = 0.37

    total power output = 10 x 2000 = 20000MW

    I'm really quite stuck now - any help is much appreciated.
    The correct answer is 12 centigrade...
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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