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Homework Help: Finding the work done by a Stirling Cycle

  1. Nov 12, 2016 #1
    1. Given the following p-V diagram of an ideal Stirling Cycle, determine the theoretical values of W12, Q12, W34 and Q34 in terms of T1, T2, V1, V2, n (the number of moles) and R (the universal gas constant). Determine the total theoretical p-V work W12341 for the full cycle.

    2. dU = dQ-Pdv

    3. I've only just started thermodynamics recently, so my grasp on it is still very weak. I've tried finding W12 using W = -∫pdV but I'm not really sure how that gives me theoretical work. I think I'm supposed to end up with some sort of numerical answer for the final part to compare it with an actual p-V work value and find the efficiency of the Stirling Engine. de424315a5395941d2365d8e794de16e.png
  2. jcsd
  3. Nov 12, 2016 #2


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    When you write W12 = - ∫p dV, both p and V are changing from 1 to 2. How about replacing p with something else using the ideal gas law?
  4. Nov 12, 2016 #3


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    The working fluid in an ideal Stirling cycle engine goes through four processes :

    Compression at constant temperature .
    Heat addition at constant volume .
    Expansion at constant temperature .
    Heat removal at constant volume .

    Can you identify the four processes on your diagrams ?

    What formulas apply to each process ?

    Reading material :

    Stirling Cycle
    Constant temperature process
    Constant volume process
    Last edited: Nov 12, 2016
  5. Nov 12, 2016 #4
    Oh thank you! Your response was very illuminating. I hope you don't mind but I'd just like to check I've got this right:
    For Isothermal Expansion : W = nRTln[Vf/Vi]
    For Isothermal Compression: W = - nRTln[Vf/Vi]
    For Heat Addition: Q = nCvΔT
    For Heat Removal: Q = - nCvΔT
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