Carnot Efficiency: Qh/Ql=Th/Tl Explained

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    Carnot Efficiency
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Discussion Overview

The discussion revolves around the derivation of the Carnot efficiency equation, specifically the relationship Qh/Ql = Th/Tl. Participants express frustration over the lack of explanation in textbooks and seek clarification on the underlying principles and equations involved in this concept.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests help in understanding the derivation of the Carnot efficiency equation, expressing frustration with textbook explanations.
  • Another participant discusses the Carnot cycle and mentions that heat absorption and rejection occur during isothermal processes, providing equations related to heat and volume ratios.
  • Some participants suggest that the equation can be derived from the first law of thermodynamics, specifically using the equations for internal energy and work done during isothermal processes.
  • There is mention of the relationship between pressure, volume, and temperature in isothermal conditions, although the implications of these relationships are not fully resolved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the derivation of the Carnot efficiency equation, with multiple viewpoints and approaches presented. The discussion remains unresolved regarding the clarity and completeness of the derivation process.

Contextual Notes

Some assumptions regarding the conditions of the Carnot cycle and the applicability of certain equations are not explicitly stated, which may affect the understanding of the derivation. The discussion includes references to specific equations and principles without fully resolving their interconnections.

John Pang
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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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