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Homework Help: Heat engine

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data
    I need some help with this problem:

    A model Stirling engine uses n = 7.44 × 10–3 mol of gas (assumed to be ideal) as a working substance. It operates between a high temperature reservoir at TH= 95.0°C and a low temperature reservoir at Tc = 24.0°C. The volume of its working substance doubles during each expansion stroke. It runs at a rate of 0.6 cycles per second. Assume the engine is ideal.

    How much Work does the engine do per cycle (include the sign)?

    2. Relevant equations

    [tex]W=nRT ln \frac{V_i}{V_f}[/tex]

    3. The attempt at a solution

    Using the formula above I get

    (7.44 × 10-3)(8.314) T ln (vi/2vi)

    But I don't know how to continue since I don't know the value for the initial volume or temprature and I don't know how to find them... I mean for the temprature at least, I'm given two different tempratures TH and Tc and I don't see which one to use!
     
  2. jcsd
  3. Apr 4, 2010 #2

    ideasrule

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    Homework Helper

    The volume doubles, so Vi/Vf = 1/2 for the expansion processes and Vi/Vf=2 for the compression process.

    Take a look at this graph: http://upload.wikimedia.org/wikipedia/commons/2/25/Stirling_Cycle.svg

    You have to calculate the work done for each leg and add them together to calculate total work. The expansion/compression legs are isothermal, so there's only one T.
     
  4. Apr 5, 2010 #3
    THANK YOU! It makes perfect sense now. :smile: But I have another question; what if they ask 'what is the Power of the engine?'

    Should we just divide the total work done (that we just calculated) by the number of cycles per second? I tried that but it didn't give me the correct answer...
     
  5. Apr 5, 2010 #4
    You should multiply the work with the number of cycles per second, cause P = Q/t and Q = W(one cycle) * (cycles in a second) if t = 1 sec.
     
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