Carnot Efficiency: Qh/Ql=Th/Tl Explained

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    Carnot Efficiency
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SUMMARY

The discussion focuses on the derivation of the Carnot efficiency equation, Qh/Ql = Th/Tl, which relates the heat absorbed and rejected during isothermal processes in a Carnot cycle. Participants explain that the heat exchange occurs at constant temperature, and the relationship can be derived using the equations for internal energy (U = 3/2nRT) and the first law of thermodynamics (ΔU = Q - W). The derivation involves applying adiabatic equations and understanding the isothermal processes where dU = 0, leading to the conclusion that Q1/Q2 = -T1/T2.

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  • Carnot cycle principles
  • Thermodynamic laws, particularly the first law
  • Understanding of isothermal and adiabatic processes
  • Basic knowledge of equations of state, such as U = 3/2nRT
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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 doesn't explain this.
 
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John Pang said:
according to catnot efficiency, Qh/Ql=Th/Tl .Can anyone help explain how is this equation derived? It is really frustrating as my textbook doesn't explain this.

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>
 
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Thx. So it can be easily derived from the equations U=3/2nRT , and change in U= Change in Q - W, right?
 
John Pang said:
Thx. So it can be easily derived from the equations U=3/2nRT , and change in U= Change in Q - W, right?

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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