7.1

ME 200 –Thermodynamics I

Lecture 34: Exergy Analysis-

Concept

Yong Li

Shanghai Jiao Tong University

Institute of Refrigeration and Cryogenics

800 Dong Chuan Road Shanghai, 200240, P. R. China

Email : liyo@sjtu.edu.cn

Phone: 86-21-34206056; Fax: 86-21-34206056

7.2

Previous energy analysis

All considered the isentropic process as the goal to

strive for.

Maximize adiabatic and isentropic efficiency

This approach is short sighted for three reasons:

1. It ignores processes where heat transfer is

present.(The majority of all practical processes.)

2. It assumes that reversibility can be obtained.

3. It assumes that the exit state of a device can

“float”, i.e., cases where the exit pressure is

fixed, but the exit temperature is allowed to fall

below the temperature of the surroundings.

Not so real!

7.3

Example

potential for use, not conserved

Exergy (Availability) Analysis

7.4

Exergy reference environment and dead state

Exergy reference environment:::Large enough portion of

system (CM1) surroundings such that intensive properties (e.g., T0,

p0) are unaffected by interaction with the system (CM2).

» Simple compressible system

»ΔUe = T0 ΔSe - p0 ΔVe Eq(6.10)

» ΔKE = 0, ΔPE=0

Dead state ::: State of system (CM2) when in thermodynamic

equilibrium with the environment (T0 and p0)

» Still possess energy?

Closed

System

Environment @ To,po

Qi

CM2

CM1

Wi

Wuse

Concepts

7.5

Defining exergy

Systems A B (equilibrium): work

Notes:

» Wc = net useful work of

combined system and

environment (CM1)!

» The goal is to maximize

Wc!

Boundary of the combined

system.

Exergy/Availability ::: Maximum

theoretical work output that could

be done by a system if it were to

come into equilibrium with its

environment!

Exergy- E (J)

Concepts

7.6

Exergy Analysis for Closed Systems

1st law Total Energy for CM1:

Assumptions

» Maximize Wc final state of CM1 is the dead state

» Neglect DKECM1 and DPECM1

» Sole effect is work out Qc = 0

c c cE Q WD

c c cW E U D D

0

7.7

Continue Exergy Analysis for Closed Systems

The changes in energy of the combined

system can be calculated by:

Substitution into the equation for useful

work leads to:

2( )c o CM eE U E UD D

Constant for environment

0 2 0 0( ) ( )c CM o eW E U p V V T S D

c cW E D

Exergy reference environment ΔUe = T0ΔSe - p0 ΔVe

2 0 0( ) ( )c o CM e eE U E T S p VD D D

7.8

Continue Exergy Analysis for Closed Systems

Note:

ΔVe = – ΔVCM2

and ΔSc=c=ΔSCM1 = ΔSCM2 + Δse

ΔSe = ΔSCM1 – ΔSCM2 = ΔSCM1 – (S0– S)CM2

= ΔSCM1 + (S – S0)CM2

Then, substituting ΔVe and ΔSe into the equation for useful

work:

Wc = (E – U0)CM2 + p0(V – V0)CM2

– T0 (S – S0)CM2 – T0ΔSCM1

= – (V0 – V)CM2 = (V – V0)CM2

0 2 0 0( ) ( )c CM o eW E U p V V T S D

7.9

Continue Exergy Analysis for Closed Systems

In order to maximize Wc, assume a reversible process for

CM1 and thus, ΔSCM1 = 0!

In addition, drop the subscript CM2:

Wrev,c,max = E– U0 + p0 (V – V0) – T0 (S – S0)

Definition of closed system exergy (availability):

E = Wrev,c,max

Wc = (E – U0)CM2 + p0(V – V0)CM2– T0 (S – S0)CM2 – T0ΔSCM1

E = E – U0 + p0(V – V0) – T0 (S – S0)

7.10

Continue Exergy Analysis for Closed Systems

In specific terms:

e o o o o oe u p v v T s s

Change in Exergy:

2 1 o 2 1 o 2 1U U p V V T S S2 1E = E -ED

2 / 2e o o o o ou V gz u p v v T s s

2 / 2e o o o o ou u p v v T s s V gz

7.11

Notes for Exergy Analysis

It can be used for both adiabatic and non-adiabatic

processes.

It shows how close a device operating between two

fixed end states is to its optimum performance.

It identifies the system components most responsible

for sub-optimum system performance.

7.12

Notes on exergy

Exergy is a measure of the departure of the state of a system

from that of the environment.

Exergy can be regarded as a property of the system, once

the environment is specified.

Exergy cannot be negative!

Exergy is not conserved but is destroyed by irreversibilities.

Exergy E does not include chemical availability.

Exergy viewed as the maximum theoretical work

Exergy can be regarded as the minimum theoretical work

input required to bring the system from the dead state to the

given state.

7.13

Closed System Exergy Balance Energy balance

Entropy balance

Multiply the entropy balance by the temperature T0 and

subtract the resulting expression from the energy balance

use the change in exergy

change

in exergy

closed system

exergy balance

7.14

Closed System Exergy Balance

Obtained by deduction from the energy and entropy balances

can be used in place of the entropy balance as an

expression of the second law.

The exergy balance can be used to determine the locations,

types, and magnitudes of energy resource waste

7.15

Closed System Exergy Balance

The value of the exergy destruction cannot be negative. It is not

a property.

destruction of

exergy

Exergy is a property

the change in exergy of a system

can be positive, negative, or zero

7.16

Closed System Exergy Rate Balance

For an isolated system, no heat or work interactions with

the surroundings occur

no transfers of exergy

the counterpart of the

increase of entropy

principle regarded as an alternative

statement of the second law

7.17

specific flow

exergy

Flow exergy

7.18

Exergy Rate Balance for Control Volumes

Closed System

Exergy Rate

Balance

specific flow

exergy