Exergy Analysis of Thermal Systems

Prof. Debajyoti BoseAlternate Energy, UPES

Exergy analysis is based on three pillars:a. Conservation of massb. Conservation of energyc. Second law of thermodynamics

Uses of exergy analysis:d. Design of thermal systemse. Reduce source of inefficiency in existing systemsf. Evaluate system economics

• Total energy associated with the system is unchanged• But initial air-fuel mixture has greater economic value and more

useful than the final product gases

• For example the fuel can be used to generate electricity or generate superheated steam

• Whereas the use of combustion product is limited

“System has greater potential in initial use.”

But once the match is lit the process is irreversibleThis shows unlike energy, EXERGY is not conserved

“Exergy can be destroyed by irreversibilities”

Defining Exergy:Exergy is the maximum theoretical work obtained as a system tends towards equilibrium.The reference environment is very important

• Suppose a steam based TPP operates around a surrounding• It is important to distinguish the environment when calculating

exergy

• For exergy analysis we introduce “immediate environment.” Where intensive property may vary for the system

• However, it is unaffected by the environment

Without the Exergy Line = Energy analysis of TPP

Exergy of a system:

where E= (U+ KE + PE)

U0, V0, and S0 are the values of the same properties if the system were at the dead state

“The units of exergy are seen to be the same as those of energy.”

Dead State:

• If the state of a fixed quantity of matter, a closed system, departs from that of the environment, an opportunity exists for developing work. However, as the system changes state toward that of the environment, the opportunity diminishes, ceasing to exist when the two are in equilibrium with one another. This state of the system is called the dead state

• At the dead state, the fixed quantity of matter under consideration is imagined to be sealed in an envelope impervious to mass flow, at rest relative to the environment, and internally in equilibrium at the temperature T0 and pressure p0 of the environment

• At the dead state, both the system and environment possess energy, but the value of exergy is zero because there is no possibility of a spontaneous change within the system or the environment, nor can there be an interaction between them

EXERGY Aspects:

• Exergy is a measure of the departure of the state of a system from that of the environment.It is therefore an attribute of the system and environment together

• The value of exergy cannot be negative. If a system were at any state other than the dead state, the system would beable to change its condition spontaneously toward the deadState

• Exergy is not conserved but is destroyed by irreversibilities.

The specific exergy on a unit mass basis is given by:

we can determine the change in exergy between two states of a closed system as the difference:

By inspection, the units of specific exergy are the same as those of specific energy.

Numericals1. Determine the specific exergy of saturated water vapor at 120°C, having a velocity of 30 m/s and an elevation of 6 m, each relative to an exergy reference environment where T0 = 298 K (25°C), p0= 1 atm, and g = 9.8 m/s2. For water as saturated vapor at 120°C, Given v = 0.8919 m3/kg, u= 2529.3 kJ/kg, s= 7.1296 kJ/kg K. At the dead state, where T0 = 298°K (25C) and p0 = 1 atm, water is a liquid.

• Additional Data given:

2. A cylinder of an internal combustion engine contains 2450 cm3 of gaseous combustion products at a pressure of 7 bar and a temperature of 867°C just before the exhaust valve opens. Determine the specific exergy of the gas, in kJ/kg. Ignore the effects of motion and gravity, and model the combustion products as air as an ideal gas. Take T0= 300 K (27°C) and p0=1.013 bar.