Thermodynamics - Cycle efficiency

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SUMMARY

The discussion focuses on calculating the efficiency of a thermodynamic cycle involving isothermic and adiabatic processes. The efficiency, denoted as η, is defined by the equation η = 1 - Qc / Qh, where Qh is the heat input and Qc is the heat output. Participants emphasize using the fundamental efficiency equation (efficiency = W/Qh) instead of the Carnot efficiency equation, and highlight the importance of understanding the physical interpretation of the area enclosed by the cycle on a Temperature vs. Entropy (T-S) graph. Caution is advised regarding cycles with sloping straight line paths, as they complicate efficiency calculations.

PREREQUISITES
  • Understanding of thermodynamic processes, specifically isothermic and adiabatic processes.
  • Familiarity with the concepts of heat transfer (Qh and Qc) in thermodynamics.
  • Knowledge of Temperature-Entropy (T-S) diagrams and their physical interpretations.
  • Basic proficiency in calculating work output from thermodynamic cycles.
NEXT STEPS
  • Study the derivation and application of the fundamental efficiency equation in thermodynamics.
  • Learn how to analyze and interpret Temperature-Entropy (T-S) diagrams for various cycles.
  • Explore the complexities of efficiency calculations for cycles with sloping straight line paths on PV diagrams.
  • Read advanced thermodynamics textbooks that cover cycle efficiency and related concepts in detail.
USEFUL FOR

Students and professionals in mechanical engineering, thermodynamics enthusiasts, and anyone involved in analyzing or optimizing thermodynamic cycles.

Jalo
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Homework Statement



Compute the efficiency of the following cycle:

291j1ft.png


Homework Equations





The Attempt at a Solution



I know there's an isothermic process between a and b, where heat comes into the system, let's call it Qh.
I also know that between b and c heat will leave the system, let's call it Qc.
The process from c to a is adiabatic.

The efficiency, n, is equal to:

η = 1- Qc / Qh = 1 - Qc / T2(S2-S1)

The problem is that I don't know how to compute Qc...
Any help would be highly appreciated.
Also, if anyone has a good book on the subject I'd appreciate.

Thanks.
 
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The area enclosed by a cycle on a T vs S graph has a physical interpretation that will help to determine the efficiency.
 
Thank you very much! Sadly I had no idea it had a physical interpretation..
 
Don't use Carnot efficiency equation for the cycle; but use a more fundamental and simpler equation: efficiency = (W/Qh) = (work output from the engine / heat input to the engine). The numerator is obtained from the area of the triangle. You already know how to calculate (the denominator) the heat input to the engine (T2*delta S). The ratio of the two numbers gives the efficiency.

Caution: Cycles involving sloping straight line paths can sometimes be dangerous! For eg the efficiency calculation of similar cyclic triangular paths on PV plane (instead of TS plane) is a very complicated and controversial issue.
 

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