Exergy balances

This session explains how to set up the exergy balance of a cycle.

The theory of exergy (the link below gives you access to the relevant textbook excerpt) provides a quite rigorous framework to quantify the thermodynamic quality of any system, open or closed, in steady-state or not.

It is increasingly accepted as the preferred tool to compare and optimize thermodynamic cycles, thanks to exergy balances.

It defines an integrated analysis method that includes the first two laws of thermodynamics, and thus allows us to take into account both the amount of energy put into play and its quality, which the first law cannot do.

Course reference:

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(Session realized on 06/16/11 by Renaud Gicquel)


Exergy, exergy balances



Maximum engine work


Calculation of incoming and outgoing exergies (1/2)

Calculation of incoming and outgoing exergies (2/2)

Exergy balances

Δxhi= Σk=1nxqk -Σk=1pmkΔxhk +Σk=1qτk

Exergy balances

ηx=1- Σ(Δxhij) Σ(Δxqj)+Σ(τj)

Exergy balances



Presentation of the spreadsheet

In practical terms, the exergy balance of a cycle can be established in the following manner when it is modeled in Thermoptim.

Once the model is properly set and calculated the results file can be exported (line “Export exergy calculations” of menu “Result Files”).

The first lines of this file can then be copied into the spreadsheet. You must then carefully correct by hand the part of the worksheet that makes the exergy balance, as the lines for the different processes should be constructed differently depending on whether they relate to adiabatic expansion or compression or heat exchanges with the surroundings. For the latter, you must also specify the value of the source temperature.

Finally, you should take into account the powers supplied to the system from outside. If you only have the demo version of Thermoptim you must slightly modify the spreadsheet to recalculate the exergies brought into play in the processes from the values calculated in the points screens and from the flow-rates involved, which must be copied one by one.

To facilitate the preparation of exergy balances, two documents are available from the links below:

Lecture notes on “Exergy balances” explain in detail how to proceed.

The following activities explain the structure of the spreadsheet.

Thermoptim results file

Exergy balances

Exergy balances

Exergy balances

Exergy balances

Exergy balances

Exergy balances

This session explains how to set up the exergy balance of a cycle.

It shows how to use the Thermoptim results into a spreadsheet.

We will apply this methodology to analyze quantitatively the irreversibility of various energy systems: