Exergy Analysis of a Closed System

[Soumalya]

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,

δW_HE=δQ(1-T₀/T)=δQ-T₀/T.δQ

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

but in the textbook it's given as,

δQ=δW_HE-T₀dS

Any thoughts on it?

 

[Soumalya]

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

 

[Useful nucleus]

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)

 

[Soumalya]

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?

 

[PJC01]

Exergy analysis is a powerful tool used in thermodynamics to evaluate the efficiency and sustainability of energy systems. It provides a comprehensive understanding of the energy flows and losses in a closed system, allowing for the identification of potential areas for improvement.

In the case of a closed system, where there is no flow of mass across its boundaries, the exergy analysis is based on the first and second laws of thermodynamics. The equation δQ=δWHE+T0dS is derived from the first law, which states that the change in internal energy of a closed system is equal to the heat added to the system minus the work done by the system. In this equation, δWHE represents the work done by the system and T0dS represents the change in exergy.

However, in the textbook, the equation is given as δQ=δWHE-T0dS. This may seem contradictory, but it is actually a different way of looking at the same equation. Here, δWHE represents the work done on the system, and T0dS represents the change in exergy. This equation is derived from the second law of thermodynamics, which states that the maximum work that can be obtained from a closed system is equal to the change in exergy.

Therefore, both equations are correct and can be used interchangeably in exergy analysis. It is important to understand the underlying principles and assumptions behind these equations in order to apply them correctly in different scenarios. I recommend further studying the fundamentals of thermodynamics and exergy analysis to gain a deeper understanding of this topic.