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B Carnot efficiency

  1. Mar 25, 2016 #1
    Another question, according to catnot efficiency, Qh/Ql=Th/Tl .Can anyone help explain how is this equation derived? It is really frustrating as my textbook doesnt explain this.
     
  2. jcsd
  3. Mar 25, 2016 #2
    Carnot cycle abcd ; ab and cd are the isothermals
    The heat absorbed and rejected by the system takes place during isothermal processes
    Q is of the form
    Heat absorbed /rejected in isothermal paths -NRT2 ln (Vb/Va)

    Or NRT1. ln (Vd./Vc)

    so Q1/Q2 = (T1/T2) . the ratio of the Volume factors
    But if one applies the adiabatic equations as the points b,c and a,d are connected adiabatically thereby one can get the equality of the volume factors and they cancel out
    thats why

    Q1/Q2 = -T1/T2 or Q 1/T1 +Q2/T2 = 0

    http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/img361.png
    see for details <http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node21.html>
     
  4. Mar 25, 2016 #3
    Thx. So it can be easily derived from the equations U=3/2nRT , and change in U= Change in Q - W, right?
     
  5. Mar 25, 2016 #4
    i think so as in isotherms dU =0 and Q= W (integral of PdV)
    and in isotherms P.V^gamma =constant/ or TV ^(gamma-1) = const.
     
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