Exergy Analysis of a Closed System

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Discussion Overview

The discussion focuses on the exergy analysis of a closed system as presented in the textbook "Engineering Thermodynamics" by Cengel & Boles. Participants are examining the equations related to heat transfer and entropy, specifically the sign conventions used in these equations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes a discrepancy between their derived equation for δQ and the textbook's version, suggesting δQ=δWHE+T0dS based on their interpretation.
  • Another participant points out that the textbook uses a sign convention where (-TdS= δQ), which differs from the more common convention of (TdS= δQ).
  • A participant emphasizes the importance of understanding the direction of heat transfer and its effect on entropy, stating that heat transferred to a system increases its entropy while heat transferred from a system decreases it.
  • There is a question raised about whether it is necessary to consider the sign convention when replacing δQ/T with 'dS' in equations, particularly in the context of a system rejecting heat.

Areas of Agreement / Disagreement

Participants express differing views on the sign conventions used in the equations, and there is no consensus on how to interpret the relationship between δQ and dS in this context.

Contextual Notes

Participants mention the need to consult earlier chapters of the textbook for clarification on the sign conventions, indicating that the discussion may depend on specific definitions and assumptions presented in those chapters.

Soumalya
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I was going through "Engineering Thermodynamics" by Cengel & Boles studying exergy analysis of a closed(non flow) system.Referring to the attachment as you can see the equation,

δWHE=δQ(1-T0/T)=δQ-T0/T.δQ

should give δQ=δWHE+T0dS (using dS=δQ/T)

but in the textbook it's given as,

δQ=δWHE-T0dS

Any thoughts on it?
 

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I have split the attachment and resized it for better view.Hope it's legible!
 

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For some reason this text defines the sign convention such that (-TdS= δQ). You might need to consult earlier chapters to understand why. It is more common to adopt (TdS= δQ)
 
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Useful nucleus said:
For some reason this text defines the sign convention such that (-TdS= δQ). You might need to consult earlier chapters to understand why. It is more common to adopt (TdS= δQ)

I went through the textbook again and it says,

dS=(δQ/T)int reversible

and the direction of entropy transfer depends on the direction of heat transfer i.e, heat transferred to a system increases it entropy while heat transfer from a system decreases it.

Now if I wish to replace δQ/T with 'dS' in any equation is it necessary to take into account the sign convention?

NOTE:The system is rejecting heat and thus direction of heat transfer is such that would result in a decrease in entropy of the system.So for replacing δQ/T with 'dS' should I write δQ/T=-dS?
 
Last edited:

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