Thermodynamics -- first and second law concepts

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SUMMARY

The discussion centers on evaluating four thermodynamic engines operating between constant-temperature reservoirs at 400 K and 300 K. Engines 1 and 2 violate the first law of thermodynamics, as their heat input (QH) is less than the sum of the heat rejected (QL) and work done (W). Engines 3 and 4 violate the second law of thermodynamics, which can be demonstrated by calculating the entropy changes for the reservoirs. The efficiency of these engines must not exceed 40%, in accordance with Carnot's theorem.

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  • Understanding of the first law of thermodynamics
  • Familiarity with the second law of thermodynamics
  • Knowledge of Carnot efficiency and its implications
  • Ability to calculate entropy changes in thermodynamic processes
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  • Calculate the entropy changes for engines 3 and 4 to confirm violations of the second law
  • Study the implications of Carnot efficiency on real-world engines
  • Explore the mathematical formulation of the first law of thermodynamics
  • Investigate practical applications of thermodynamic principles in engine design
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Students of thermodynamics, engineers designing thermal systems, and anyone interested in the principles governing energy conversion in engines.

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Homework Statement


An inventor claims to have invented four engines, each of which operates between constant-temperature reservoirs at 400 and 300 K. Data on each engine, per cycle of operation, can be found in the table below. Of the first and second laws of thermodynamics, which (if either) does each engine violate?
Engine |||||||||| 1 ||||||||||| 2 |||||||||| 3 |||||||||| 4
QH |||||||||||| 200J ||||| 500J||||||| 600J ||||| 100J
QL||||||||||||| -175J||||| -200J|||||| -200J|||||| -90J
W |||||||||||||||40J ||||||||400J ||||||||400J|||||||10J
Of the first and second laws of thermodynamics, which (if either) does each engine violate?

Homework Equations


should i use the efficiency rule? I know that first law says that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed. then Qh=|Qc|+W then one and two violates first law since in both Qh<|Qc|+W But how can i show that three and four violates the second law?
 
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Calculate the entropy changes for the reservoirs in cases 3 and 4.
 
Chestermiller said:
Calculate the entropy changes for the reservoirs in cases 3 and 4.
Yeah, Thanks I didn't pay attention to that at the beginning
also we could relate it to the efficiency for which it must not be greater than 40% (carnot engine)
 

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