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Calculate work from PV diagram

  1. Nov 19, 2013 #1
    1. Problem Statement

    The problem asks to find the net work from one complete cycle A-B-C. Problem 13, starting on page 66 of the slide show here:

    https://engineering.purdue.edu/~xe/Files/FE%20Review/Thermo/FEThermoReview2013.pdf [Broken]


    2. Relevant equations
    ideal gas law: PV=mRT
    Boyle's Law: W=RTln(v2/v1)

    3. Attempt at solution

    I understand most of the solution, but on page 67, says that W=R*T*ln(Vb/Va) is equivalent to W=p*Va*ln(Vb/Va), assuming ideal gas and constant mass. I don't understand why you can use volume here instead of specific volume.

    From the ideal gas law: PV=mRT and RT=PV/m. So I thought it should be W=p*Va/m*ln(Vb/Va). Why can we eliminate m here?

    Thank you!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 19, 2013 #2
    There should be an m in the equation W=R*T*ln(Vb/Va). It should read W=m*R*T*ln(Vb/Va).
     
  4. Nov 19, 2013 #3

    rude man

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    What's wrong is "W = RT ln(Vb/Va)". It should be W = mRT ln(Vb/Va).
    Notice that the wrong formula is never used in the computations.

    P.S. why do they put a slash thru the V's?
     
  5. Nov 19, 2013 #4
    One equation for isothermal work is W = m*R*T* ln(Vb/Vb). He has either made a mistake by omitting the number of moles or he has calculated the heat for 1 mole.
     
  6. Nov 19, 2013 #5
    Thanks for the responses. Good to know I'm not crazy.

    In the reference material for the fundamentals of engineering exam, the formula also does not include mass. I guess its a typo. Maybe that's where the author of the presentation got the formula from.

    I think it is to differentiate between volume and specific volume. It confused me at first though.
     
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