Does the Entropy Change in a Carnot Cycle Sum to Zero?

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SUMMARY

The entropy change in a Carnot cycle sums to zero for the entire system, which includes the engine and the two thermal reservoirs. This conclusion is based on the Clausius theorem, which states that for a reversible cycle, the total entropy change must equal zero. Consequently, the entropy changes for the two reservoirs are equal in magnitude but opposite in sign, confirming the reversible nature of the Carnot cycle.

PREREQUISITES
  • Understanding of the Carnot cycle and its components
  • Familiarity with the Clausius theorem and its implications
  • Basic knowledge of thermodynamics and entropy
  • Ability to interpret thermodynamic diagrams and processes
NEXT STEPS
  • Study the principles of thermodynamics, focusing on the laws of thermodynamics
  • Learn about the derivation and applications of the Clausius theorem
  • Explore real-world applications of Carnot cycles in heat engines
  • Investigate the concept of entropy in irreversible processes
USEFUL FOR

Students of thermodynamics, engineers working with heat engines, and anyone interested in the principles of reversible processes in physics.

mindarson
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Is it true that for a Carnot cycle, the entropy change for the whole system (engine plus the two reservoirs) would add up to zero? I am reasoning that it would, by the Clausius theorem that for a reversible cycle (which a Carnot cycle is), the entropy change is zero. Otherwise it would not be reversible.

Is this correct? And in this case, does this mean that the entropy changes for the two reservoirs (each considered alone) are equal to each other in magnitude but opposite in sign?
 
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