Short Notes: Availability and Irreversibility | Short Notes for Mechanical Engineering PDF Download

 Page 1


Availability and Irreversibility 
The sources of energy can be divided into two groups i.e., high grade energy 
(mechanical work, electrical energy, water power, wind power) and low grade 
energy (heat or thermal energy, heat derived from nuclear fission or combustion of 
fossil fuels). That part of the low grade energy which is available for, conversion is 
referred to as available energy, while the part which is not available is known as 
unavailable energy.
Availability: When a system is subjected to a process from its original state to dead 
state the maximum amount of useful work that can be achieved under ideal 
conditions is known as available energy or availability of the system.
W m ax = AE = Q X y To(Sy-Sx)
Unavailable Energy:
UE = T0(Sy-Sx )
where, Sx and Sy are the entropy at x and y, respectively.
The Available Energy (AE) is also known as exergy and the Unavailable Energy (UE) 
as energy.
Page 2


Availability and Irreversibility 
The sources of energy can be divided into two groups i.e., high grade energy 
(mechanical work, electrical energy, water power, wind power) and low grade 
energy (heat or thermal energy, heat derived from nuclear fission or combustion of 
fossil fuels). That part of the low grade energy which is available for, conversion is 
referred to as available energy, while the part which is not available is known as 
unavailable energy.
Availability: When a system is subjected to a process from its original state to dead 
state the maximum amount of useful work that can be achieved under ideal 
conditions is known as available energy or availability of the system.
W m ax = AE = Q X y To(Sy-Sx)
Unavailable Energy:
UE = T0(Sy-Sx )
where, Sx and Sy are the entropy at x and y, respectively.
The Available Energy (AE) is also known as exergy and the Unavailable Energy (UE) 
as energy.
Available Energy from a Finite Energy Source: Consider a hot gas of mass m„ at
o o
temperature T when the environmental temperature is To. Assume that gas is 
cooled from state 1 to state 3 and heat given by the gas Qi be utilized in heating up 
reversibly a working fluid of mass mW f from state 3 to state 1. The working fluid 
expands reversibly and adiabatically in an engine or turbine from state 1 to state 2 
and then return to state 3 to complete heat engine cycle.
Available energy of a finite energy source 
Available energy = W m a x = Q 1-Q 2
= C „ (T - T 0)-T.m „ C ,, In —
= »U Cp. (T -T 0)-T , I n -
Law of Degradation of Energy
First law states that energy is always conserved quantity wise while second law 
emphasizes that energy always degrades quality wise. Second law is called the law 
of degradation of energy. Energy is always conserved but its quality is always 
degraded.
all the energy all the energy the gain in the gain in
that enters = that leaves + reversible + irreversible
the system the system energy enerav
L
Reversible work by an open system exchanging heat only with the surroundings.
, . v~ , F.:
dTT^ = dm ,
\ ~ ^ gZ.
— dm. h, — TtS2 gZ2
-d
J?IV"
U~T,S-\----- + mgZ
Where, Z\ and Z2 are the elevation at 1 and 2, respectively. 
For steady flow process, = > dm7 =dm2 dm
dEv=0
The maximum reversible work
. r,:
~T-S: — y - y Z ,
The expression is called Kennan function B. In term of per unit mass is called 
Kennan function 8.
Page 3


Availability and Irreversibility 
The sources of energy can be divided into two groups i.e., high grade energy 
(mechanical work, electrical energy, water power, wind power) and low grade 
energy (heat or thermal energy, heat derived from nuclear fission or combustion of 
fossil fuels). That part of the low grade energy which is available for, conversion is 
referred to as available energy, while the part which is not available is known as 
unavailable energy.
Availability: When a system is subjected to a process from its original state to dead 
state the maximum amount of useful work that can be achieved under ideal 
conditions is known as available energy or availability of the system.
W m ax = AE = Q X y To(Sy-Sx)
Unavailable Energy:
UE = T0(Sy-Sx )
where, Sx and Sy are the entropy at x and y, respectively.
The Available Energy (AE) is also known as exergy and the Unavailable Energy (UE) 
as energy.
Available Energy from a Finite Energy Source: Consider a hot gas of mass m„ at
o o
temperature T when the environmental temperature is To. Assume that gas is 
cooled from state 1 to state 3 and heat given by the gas Qi be utilized in heating up 
reversibly a working fluid of mass mW f from state 3 to state 1. The working fluid 
expands reversibly and adiabatically in an engine or turbine from state 1 to state 2 
and then return to state 3 to complete heat engine cycle.
Available energy of a finite energy source 
Available energy = W m a x = Q 1-Q 2
= C „ (T - T 0)-T.m „ C ,, In —
= »U Cp. (T -T 0)-T , I n -
Law of Degradation of Energy
First law states that energy is always conserved quantity wise while second law 
emphasizes that energy always degrades quality wise. Second law is called the law 
of degradation of energy. Energy is always conserved but its quality is always 
degraded.
all the energy all the energy the gain in the gain in
that enters = that leaves + reversible + irreversible
the system the system energy enerav
L
Reversible work by an open system exchanging heat only with the surroundings.
, . v~ , F.:
dTT^ = dm ,
\ ~ ^ gZ.
— dm. h, — TtS2 gZ2
-d
J?IV"
U~T,S-\----- + mgZ
Where, Z\ and Z2 are the elevation at 1 and 2, respectively. 
For steady flow process, = > dm7 =dm2 dm
dEv=0
The maximum reversible work
. r,:
~T-S: — y - y Z ,
The expression is called Kennan function B. In term of per unit mass is called 
Kennan function 8.
IT'
I, w\r , , *«v: _
= ft--- ^-+mgZl - ft--- — - mgZ:
= W - V2
Where, V7 is called the availability function of a steady flow process given by
, , m\' , „
J J = O --------r msZ
If AKE = 0 and APE = 0
Wm ax = bi -b2 = (f> 1 - f> 2)"fo(Sl-S2)
Maximum reversible work for a closed system, 
dm i = dm2 = 0
d it; - d U
T <- , f f l V ~ , 7
T r.S T — — + fflgZ
where, at
AKE=0, APE=0 Wm ax = (Ur T0Si)-(U2-T0S2)e 
where, A KE = Change in kinetic energy 
A PE = Change in potential energy 
Maximum reversible work for unit mass of fluid,
Wmax = (U v T 0S M U 2-T 0S 2)
Useful Work
Maximum useful work Wm ax=Wm ax-po(l/2-^i)
Vi and V2 are the initial and final volumes of the systems and po is the atmospheric 
pressure.
Useful Work for Unsteady Open System
f i
V-
dWv )-dmx\ hi~TtS i + ~ + gZl ¦-dm, \ k:- T.S, h —^-+gZ2
- d
rri V
L’ + p.V-T:S +——+ mgZ
Useful Work for Unsteady Closed System
[Vrr) = -d U+pJ'-TS + ^ - + mgZ
= - d [E +PiV — I S ]
i X ’ U = £ , - £ :+ P o (Ii-K )-r0(Si-S,)
AKE=0, APE=0
(Wu )m ax = Ui-U2+p0(Vi-V2)-T0(Si-S2)
(Wu )m ax = (Ui+p0V-T0Si)-(U2+p0V2-T0S2)
(Wu ) m ax = < p r< p 2 < | ) is called the availability function for a closed system,
(p = U + p0V -p0S
or q > = u + p0V - p0S (per unit mass basis)
Maximum useful work obtainable when the systems exchange heat with thermal 
reservoirs in addition to the atmosphere
Page 4


Availability and Irreversibility 
The sources of energy can be divided into two groups i.e., high grade energy 
(mechanical work, electrical energy, water power, wind power) and low grade 
energy (heat or thermal energy, heat derived from nuclear fission or combustion of 
fossil fuels). That part of the low grade energy which is available for, conversion is 
referred to as available energy, while the part which is not available is known as 
unavailable energy.
Availability: When a system is subjected to a process from its original state to dead 
state the maximum amount of useful work that can be achieved under ideal 
conditions is known as available energy or availability of the system.
W m ax = AE = Q X y To(Sy-Sx)
Unavailable Energy:
UE = T0(Sy-Sx )
where, Sx and Sy are the entropy at x and y, respectively.
The Available Energy (AE) is also known as exergy and the Unavailable Energy (UE) 
as energy.
Available Energy from a Finite Energy Source: Consider a hot gas of mass m„ at
o o
temperature T when the environmental temperature is To. Assume that gas is 
cooled from state 1 to state 3 and heat given by the gas Qi be utilized in heating up 
reversibly a working fluid of mass mW f from state 3 to state 1. The working fluid 
expands reversibly and adiabatically in an engine or turbine from state 1 to state 2 
and then return to state 3 to complete heat engine cycle.
Available energy of a finite energy source 
Available energy = W m a x = Q 1-Q 2
= C „ (T - T 0)-T.m „ C ,, In —
= »U Cp. (T -T 0)-T , I n -
Law of Degradation of Energy
First law states that energy is always conserved quantity wise while second law 
emphasizes that energy always degrades quality wise. Second law is called the law 
of degradation of energy. Energy is always conserved but its quality is always 
degraded.
all the energy all the energy the gain in the gain in
that enters = that leaves + reversible + irreversible
the system the system energy enerav
L
Reversible work by an open system exchanging heat only with the surroundings.
, . v~ , F.:
dTT^ = dm ,
\ ~ ^ gZ.
— dm. h, — TtS2 gZ2
-d
J?IV"
U~T,S-\----- + mgZ
Where, Z\ and Z2 are the elevation at 1 and 2, respectively. 
For steady flow process, = > dm7 =dm2 dm
dEv=0
The maximum reversible work
. r,:
~T-S: — y - y Z ,
The expression is called Kennan function B. In term of per unit mass is called 
Kennan function 8.
IT'
I, w\r , , *«v: _
= ft--- ^-+mgZl - ft--- — - mgZ:
= W - V2
Where, V7 is called the availability function of a steady flow process given by
, , m\' , „
J J = O --------r msZ
If AKE = 0 and APE = 0
Wm ax = bi -b2 = (f> 1 - f> 2)"fo(Sl-S2)
Maximum reversible work for a closed system, 
dm i = dm2 = 0
d it; - d U
T <- , f f l V ~ , 7
T r.S T — — + fflgZ
where, at
AKE=0, APE=0 Wm ax = (Ur T0Si)-(U2-T0S2)e 
where, A KE = Change in kinetic energy 
A PE = Change in potential energy 
Maximum reversible work for unit mass of fluid,
Wmax = (U v T 0S M U 2-T 0S 2)
Useful Work
Maximum useful work Wm ax=Wm ax-po(l/2-^i)
Vi and V2 are the initial and final volumes of the systems and po is the atmospheric 
pressure.
Useful Work for Unsteady Open System
f i
V-
dWv )-dmx\ hi~TtS i + ~ + gZl ¦-dm, \ k:- T.S, h —^-+gZ2
- d
rri V
L’ + p.V-T:S +——+ mgZ
Useful Work for Unsteady Closed System
[Vrr) = -d U+pJ'-TS + ^ - + mgZ
= - d [E +PiV — I S ]
i X ’ U = £ , - £ :+ P o (Ii-K )-r0(Si-S,)
AKE=0, APE=0
(Wu )m ax = Ui-U2+p0(Vi-V2)-T0(Si-S2)
(Wu )m ax = (Ui+p0V-T0Si)-(U2+p0V2-T0S2)
(Wu ) m ax = < p r< p 2 < | ) is called the availability function for a closed system,
(p = U + p0V -p0S
or q > = u + p0V - p0S (per unit mass basis)
Maximum useful work obtainable when the systems exchange heat with thermal 
reservoirs in addition to the atmosphere
h, -T,S. — mgZ,
mvz
U — T:S 4— ------mgZ 1 - i
Tx
TE — Temperature of resen'oir 
Q_ — Heat received bv system
Dead State: When the system is in equilibrium with surrounding with temperature 
To and pressure po and the system also in chemical equilibrium with zero velocity 
and minimum potential energy. Then, it is called the dead state. All spontaneous 
processes terminate at the dead state.
Irreversibility
The actual work done by a system is always less than idealized reversible work and 
the difference between the two is called the irreversibility of the process.
l = Wmax-W
I = To(ASS ystem + ASsu rro u n cjin g)
/ = To(AS)universal
7o(AS)universai represent an increase in unavailable energy.
Goby-Stodola Theorem: It states that the rate of loss of available energy or exergy 
in a process is proportional to the rate of entropy generation Sg en
I = W|ost = ToASuniversa|
/ = T o S g en
Insulation
© / ©
• ¦ - > ' v l- • • 4
* i
» * *
---- !-^ ----{-?
I t
W . - 7 / ¦ / / , S'/V/i A > V A ' - Z ’ .V A V / Z V / S / / /
Goby-Stodola theorem
where, / = irreversibility
Irreversibility for adiabatic flow of an ideal gas through the segment of pipe with 
friction decreases in availability and is proportional to pressure drop and mass flow 
rate.
I = = T.St(. - / = mRT, r E
ft
• The term Kennan function B(=H-ToS) is used in steady flow process and 
availability function is given by
mgZ
• For closed system availability function is given by
= U + p cV — PrS
Page 5


Availability and Irreversibility 
The sources of energy can be divided into two groups i.e., high grade energy 
(mechanical work, electrical energy, water power, wind power) and low grade 
energy (heat or thermal energy, heat derived from nuclear fission or combustion of 
fossil fuels). That part of the low grade energy which is available for, conversion is 
referred to as available energy, while the part which is not available is known as 
unavailable energy.
Availability: When a system is subjected to a process from its original state to dead 
state the maximum amount of useful work that can be achieved under ideal 
conditions is known as available energy or availability of the system.
W m ax = AE = Q X y To(Sy-Sx)
Unavailable Energy:
UE = T0(Sy-Sx )
where, Sx and Sy are the entropy at x and y, respectively.
The Available Energy (AE) is also known as exergy and the Unavailable Energy (UE) 
as energy.
Available Energy from a Finite Energy Source: Consider a hot gas of mass m„ at
o o
temperature T when the environmental temperature is To. Assume that gas is 
cooled from state 1 to state 3 and heat given by the gas Qi be utilized in heating up 
reversibly a working fluid of mass mW f from state 3 to state 1. The working fluid 
expands reversibly and adiabatically in an engine or turbine from state 1 to state 2 
and then return to state 3 to complete heat engine cycle.
Available energy of a finite energy source 
Available energy = W m a x = Q 1-Q 2
= C „ (T - T 0)-T.m „ C ,, In —
= »U Cp. (T -T 0)-T , I n -
Law of Degradation of Energy
First law states that energy is always conserved quantity wise while second law 
emphasizes that energy always degrades quality wise. Second law is called the law 
of degradation of energy. Energy is always conserved but its quality is always 
degraded.
all the energy all the energy the gain in the gain in
that enters = that leaves + reversible + irreversible
the system the system energy enerav
L
Reversible work by an open system exchanging heat only with the surroundings.
, . v~ , F.:
dTT^ = dm ,
\ ~ ^ gZ.
— dm. h, — TtS2 gZ2
-d
J?IV"
U~T,S-\----- + mgZ
Where, Z\ and Z2 are the elevation at 1 and 2, respectively. 
For steady flow process, = > dm7 =dm2 dm
dEv=0
The maximum reversible work
. r,:
~T-S: — y - y Z ,
The expression is called Kennan function B. In term of per unit mass is called 
Kennan function 8.
IT'
I, w\r , , *«v: _
= ft--- ^-+mgZl - ft--- — - mgZ:
= W - V2
Where, V7 is called the availability function of a steady flow process given by
, , m\' , „
J J = O --------r msZ
If AKE = 0 and APE = 0
Wm ax = bi -b2 = (f> 1 - f> 2)"fo(Sl-S2)
Maximum reversible work for a closed system, 
dm i = dm2 = 0
d it; - d U
T <- , f f l V ~ , 7
T r.S T — — + fflgZ
where, at
AKE=0, APE=0 Wm ax = (Ur T0Si)-(U2-T0S2)e 
where, A KE = Change in kinetic energy 
A PE = Change in potential energy 
Maximum reversible work for unit mass of fluid,
Wmax = (U v T 0S M U 2-T 0S 2)
Useful Work
Maximum useful work Wm ax=Wm ax-po(l/2-^i)
Vi and V2 are the initial and final volumes of the systems and po is the atmospheric 
pressure.
Useful Work for Unsteady Open System
f i
V-
dWv )-dmx\ hi~TtS i + ~ + gZl ¦-dm, \ k:- T.S, h —^-+gZ2
- d
rri V
L’ + p.V-T:S +——+ mgZ
Useful Work for Unsteady Closed System
[Vrr) = -d U+pJ'-TS + ^ - + mgZ
= - d [E +PiV — I S ]
i X ’ U = £ , - £ :+ P o (Ii-K )-r0(Si-S,)
AKE=0, APE=0
(Wu )m ax = Ui-U2+p0(Vi-V2)-T0(Si-S2)
(Wu )m ax = (Ui+p0V-T0Si)-(U2+p0V2-T0S2)
(Wu ) m ax = < p r< p 2 < | ) is called the availability function for a closed system,
(p = U + p0V -p0S
or q > = u + p0V - p0S (per unit mass basis)
Maximum useful work obtainable when the systems exchange heat with thermal 
reservoirs in addition to the atmosphere
h, -T,S. — mgZ,
mvz
U — T:S 4— ------mgZ 1 - i
Tx
TE — Temperature of resen'oir 
Q_ — Heat received bv system
Dead State: When the system is in equilibrium with surrounding with temperature 
To and pressure po and the system also in chemical equilibrium with zero velocity 
and minimum potential energy. Then, it is called the dead state. All spontaneous 
processes terminate at the dead state.
Irreversibility
The actual work done by a system is always less than idealized reversible work and 
the difference between the two is called the irreversibility of the process.
l = Wmax-W
I = To(ASS ystem + ASsu rro u n cjin g)
/ = To(AS)universal
7o(AS)universai represent an increase in unavailable energy.
Goby-Stodola Theorem: It states that the rate of loss of available energy or exergy 
in a process is proportional to the rate of entropy generation Sg en
I = W|ost = ToASuniversa|
/ = T o S g en
Insulation
© / ©
• ¦ - > ' v l- • • 4
* i
» * *
---- !-^ ----{-?
I t
W . - 7 / ¦ / / , S'/V/i A > V A ' - Z ’ .V A V / Z V / S / / /
Goby-Stodola theorem
where, / = irreversibility
Irreversibility for adiabatic flow of an ideal gas through the segment of pipe with 
friction decreases in availability and is proportional to pressure drop and mass flow 
rate.
I = = T.St(. - / = mRT, r E
ft
• The term Kennan function B(=H-ToS) is used in steady flow process and 
availability function is given by
mgZ
• For closed system availability function is given by
= U + p cV — PrS
and
a = 4 ~ § >
where
f = l \ + P c , V o - T 0S c
Property Helmholty function F-be defined by the relation F = U - TS 
Given function G is defined as G=H-TS=U+pV-TS