Efficiency of a heat engine given a P-V diagram of its process

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SUMMARY

The discussion centers on the efficiency of a heat engine as represented by a P-V diagram. Participants emphasize the importance of clearly presenting equations, specifically requesting the use of LaTeX for clarity. The focus is on ensuring that the mathematical representation of the heat engine's processes is understandable for accurate analysis and discussion.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat engine cycles.
  • Familiarity with P-V diagrams and their significance in thermodynamic processes.
  • Proficiency in LaTeX for formatting equations clearly.
  • Knowledge of efficiency calculations for heat engines.
NEXT STEPS
  • Research the laws of thermodynamics and their application to heat engines.
  • Learn how to create and interpret P-V diagrams for various thermodynamic processes.
  • Practice writing equations in LaTeX for clear mathematical communication.
  • Explore methods for calculating the efficiency of different types of heat engines.
USEFUL FOR

Students and professionals in mechanical engineering, thermodynamics researchers, and anyone involved in the design or analysis of heat engines.

XSummer32
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Homework Statement
Hello, I'm attempting a question and I'm not sure what I did wrong with my answer
This is the question:

A volume of ideal gas, Cv = 1.21R, undergoes a cyclic process, the triangle abc in the p-V diagram. It starts at point a (T = 300 K, P = 3 kPa, V = 1 L) and expands until the volume reaches 6.3 liter at point b. It then gives away heat to the environment at constant pressure until its volume decreases to point c (P = 1 kPa, V = 1 L). Finally, it absorbs heat at constant volume and gets back to point a. Find the efficiency (%) of this heat engine.

(hint: find the total net work (W) done, and identify the processes (ab and ca) in which the gas absorbs a total amount of heat Qh. The efficiency is then W/Qh.
Relevant Equations
Q - isothermal = nRT ln(v2/v1)
volume constant = nCv * Change in Temperature

Work done - Isothermal = -nRT ln (v2/v1)
Isobaric = -P * Change in volume

Efficiency = W/Qh
I post the working in the attached file
 

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I can't read your handwriting; your post is unreadable. Just write out your last two equations using LaTex, and I'll see what you've come up with.
 

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