Exergy or Availability Balances

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Introduction

The First Law of Thermodynamics tells us that energy is conserved.
The Second Law of Thermodynamics tells us that real processes are irreversible and that entropy is generated.

By combining the First and Second Laws, we can determine:

  • the maximum possible useful work obtainable from a system
  • how much work is lost due to irreversibilities
  • the thermodynamic efficiency of real processes

The quantity that measures this maximum possible work is called exergy or availability.

Exergy analysis is often called Second-Law analysis, although it actually uses both the First and Second Laws together.

The Law is a Thief: It Destroys Exergy and Laughs in Your Face Part 1

This video derives the Combined 1st and 2nd Laws and develops forms for

  • closed systems
  • open steady-state systems
  • open transient systems

It also introduces the concepts of ideal work, lost work, and thermodynamic efficiency.

Visuals

The Law is a Thief: It Destroys Exergy and Laughs in Your Face Part 2

This video presents a detailed example applying the Combined 1st and 2nd Laws to a Linde cycle system for condensing methane.

Visuals

Examples and Definitions

Examples

Definitions

Lost Work, \(\dot{W}_\mathrm{lost}\)
The work that could have been produced but was lost because of irreversibilities.

It is related to entropy generation by

\[ \dot W_\mathrm{lost} = T_\sigma \dot S_\mathrm{gen} \]

where \(T_\sigma\) is the ambient temperature.

Alternate symbols used in the literature for the ambient temperature include
\(T_0\) and \(T_\infty\).

Actual Work, \(\dot{W}_s\)
The work actually produced or consumed by the system.
Entropy Generation Rate, \(\dot{S}_\mathrm{gen}\) or \(\dot{S}_G\)
The rate of entropy generation caused by irreversibilities in the system and surroundings.

For any real process

\[ \dot S_\mathrm{gen} > 0 \]

Ideal Work, \(\dot{W}_\mathrm{ideal}\)
The work that would be obtained if the process were completely reversible.
Exergy
The maximum possible useful work obtainable from a system relative to a specified environment.
Availability
Another name for exergy, used by some authors.
Note

Ideal work, exergy, and availability are closely related concepts describing the maximum useful work obtainable relative to the environment.

Second-Law Analysis
An analysis using the combined First and Second Laws to determine ideal work and the work lost due to irreversibilities.

Thermodynamic (\(\eta_\mathrm{T}\)) or Second-Law (\(\eta_\mathrm{II}\)) Efficiency

For systems that produce work

\[ \eta_\mathrm{T} = \frac{\dot W_s}{\dot W_\mathrm{ideal}} \]

For systems that require work

\[ \eta_\mathrm{T} = \frac{\dot W_\mathrm{ideal}}{\dot W_s} \]