Entropy

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Made by:
Assistant Professor : NAPHIS AHAMAD
MECHANICAL ENGINEERING
6/10/2017Naphis Ahamad (ME) JIT 1

*
Made by:
Assistant Professor : NAPHIS AHAMAD
MECHANICAL ENGINEERING

*

6/10/2017NAPHIS AHAMAD(ME)JIT 4
Entropy
 The 2nd law states that process occur in a certain direction,
not in any direction.
 It often leads to the definition of a new property called
entropy, which is a quantitative measure of disorder for a
system.
 Entropy can also be explained as a measure of the
unavailability of heat to perform work in a cycle.
 This relates to the 2nd law since the 2nd law predicts that
not all heat provided to a cycle can be transformed into an
equal amount of work, some heat rejection must take place.

Entropy Change
 The entropy change during a reversible process is defined as
 For a reversible, adiabatic process
dS
S S


0
2 1
 The reversible, adiabatic process is called an isentropic
process.

Entropy Change and Isentropic Processes
The entropy-change and isentropic relations for a process can be
summarized as follows:
i. Pure substances:
Any process: Δs = s2 – s1 (kJ/kgK)
Isentropic process: s2 = s1
ii. Incompressible substances (liquids and solids):
Any process: s2 – s1 = cav T2/T1 (kJ/kg
Isentropic process: T2 = T1

iii. Ideal gases:
a) constant specific heats (approximate treatment):
s s C
T
T
R
v
v
v av2 1
2
1
2
1
  , ln ln
2 2
2 1 ,
1 1
ln lnp av
T P
s s C R
T P
  
for isentropic process
2 1
1 2.
k
s const
P v
P v
   
   
   
for all process

Isentropic Efficiency for Turbine

Isentropic Efficiency for Compressor

Example
Steam at 1 MPa, 600°C,
expands in a turbine to 0.01
MPa. The isentropic work of
the turbine is 1152.2 kJ/kg. If
the isentropic efficiency of the
turbine is 90 percent, calculate
the actual work. Find the actual
turbine exit temperature or
quality of the steam.
Solution:
 
1 2
,
1 2
,
0.9 1153
1037.7
a a
isen T
s s
a isen T s
kJ
kg
w h h
w h h
w w



 

 


 Theoretically:

11
1 1 .
2
2
2 1 .
2
1
3698.61
600 8.0311
2
.
0.01
0.984
8.0311
2545.6
kJ
kg
o kJ
kg K
skJ
s kg K kJ
s kg
State
hP MPa
T C s
State s
sat mixture
P MPa
x
s s
h
 

 
 

   
 Obtain h2a from Wa
1 2
2 1
2660.9
a a
a a
kJ
kg
w h h
h h w
 
 

2
2 2
2
0.01 sup
2660.9 86.85okJ
a akg
State a
P MPa erheated
h T C
 

 

*
*

*

where the equality holds for an internally reversible process and the
inequality for an irreversible process. We may conclude from these
equations that the entropy change of a closed system during an
irreversible process is greater than the integral of δQ/T evaluated for
that process. In the limiting case of a reversible process, these two
quantities become equal. We again emphasize that T in these relations is
the thermodynamic temperature at the boundary where the differential
heat δQ is transferred between the system and the surroundings.
Note that the entropy generation Sgen is always a positive quantity or
zero. Its value depends on the process, and thus it is not a property of
the system. Also, in the absence of any entropy transfer, the entropy

Equation 2 has far-reaching implications in thermodynamics. For an
isolated system (or simply an adiabatic closed system), the heat transfer
is zero, and Eq. 2 reduces to
∆Sisolated ≥ 0
This equation can be expressed as the entropy of an isolated system
during a process always increases or, in the limiting case of a reversible
process, remains constant. In other words, it never decreases. This is
known as the increase of entropy principle. Note that in the absence of

any heat transfer, entropy change is due to irreversibility's only, and their effect is always to
increase entropy.
Entropy is an extensive property, and thus the total entropy of a system is equal to the sum
of the entropies of the parts of the system. An isolated sys-tem may consist of any number of
subsystems . A system and its surroundings, for example, constitute an isolated system since
both can be enclosed by a sufficiently large arbitrary boundary across which there is no heat,
work, or mass transfer . Therefore, a system and its surroundings can be viewed as the two
subsystems of an isolated system, and the entropy change of this isolated system during a
process is the sum of the entropy changes of the system and its surroundings, which is equal
to the entropy generation since an isolated system involves no entropy transfer. That is, Sgen
= ∆Stotal = ∆Ssys + ∆Ssurr ≥ 0 ------ Eq. 3

* where the equality holds for reversible processes and the inequality for irreversible
ones. Note that Ssurr refers to the change in the entropy of the surroundings as a
result of the occurrence of the process under consideration.
* Since no actual process is truly reversible, we can conclude that some entropy is
generated during a process, and therefore the entropy of the universe, which can be
considered to be an isolated system, is continuously increasing. The more
irreversible a process, the larger the entropy generated during that process. No
entropy is generated during reversible processes (Sgen _ 0).

Entropy increase of the universe is a major concern not only to
engineers but also to philosophers, theologians, economists, and
environmentalists since entropy is viewed as a measure of the disorder
(or “mixed-up-ness”) in the universe.
The increase of entropy principle does not imply that the entropy of a
sys-tem cannot decrease. The entropy change of a system can be
negative during a process (Fig. 3), but entropy generation cannot. The
increase of entropy principle can be summarized as follows:
Sgen > 0 Irreversible process
Sgen = 0 Reversible process
Sgen < 0 Impossible process

*
Entropy of ideal gas

*

*The specific heats of ideal gases, with the exception of monatomic gases,
depend on temperature, and the integrals in Eqs. 3 and 4 cannot be
performed unless the dependence of cv and cp on temperature is known.
Even when the cv(T ) and cp(T ) functions are available, performing long
integrations every time entropy change is calculated is not practical. Then
two reasonable choices are left: either perform these integrations by simply
assuming constant specific heats or evaluate those integrals once and
tabulate the results. But here we are going to present variable specific heats
(Exact Analysis)

*

Available Energy
• There are many forms in which an energy can exist. But even under ideal
conditions all these forms can not be converted completely into work. This
indicates that energy has two parts:
-Available part
-Unavailable part
• ‘Available energy’ or‘Exergy’: is the maximum portion of energy which
could be converted into useful work by ideal processes which reduce the
system to a dead state(a state in equilibrium with the earth and its
atmosphere).
-There can be only one value for maximum work which the system alone

• ‘Unavailable energy’ orAnergy’: is the portion of energy which could
not be converted into useful work and is rejected to the surroundings
A system which has a pressure difference from that of surroundings, work
can be obtained from An expansion process, and if the system has a
different temperature, heat can be transferred to a cycle and work can
be obtained. But when the temperature and pressure becomes equal to
that of the earth, transfer of energy ceases, and although the system
contains internal energy, this energy is unavailable
•The theoretical maximum amount of work which can be obtained from a
system at any state p1 and T1 when operating with a reservoir at the
constant pressure and temperature p0 and T0 is called ‘availability’.

First Law of Thermodynamics (law of energy conservation) used for may
analyses performed Second Law of Thermodynamics simply through its
derived property - entropy (S) Other ‘Second Law’ properties my be defined
to measure the maximum amounts of work achievable from certain systems
This section considers how the maximum amount of work available from a
system, when interacting with surroundings, can be estimated All the
energy in a system cannot be converted to work: the Second Law stated
that it is impossible to construct a heat engine that does not reject energy
to the surroundings

For stability of any system it is necessary and sufficient that, in all
possible variations of the state of the system which do not alter its
energy, the variation of entropy shall be negative
• This can be stated mathematically as ∆S < 0
It can be seen that the statements of equilibrium based on energy and
entropy, namely ∆E > 0 and ∆S < 0

Availability for a Closed System (non-
steady)
All the displacement work done by a system is available to do useful work
This concept will now be generalized to consider all the possible work
outputs from a system that is not in thermodynamic and mechanical
equilibrium with its surroundings (i.e. not at the ambient, or dead state,
conditions)
The maximum work that can be obtained from a constant volume, closed
system
WS +WR = - (dU – TodS)
Hence, the maximum useful work which can be achieved from a closed system is W

This work is given the symbol dA
Since the surroundings are at fixed pressure and temperature (i.e. po
and To are constant) dA can be integrated to give
A = U + po V - TOS
A is called the non-flow availability function
It is a combination of properties
A is not itself a property because it is defined in relation to the arbitrary
datum values of po and To It is not possible to tabulate values of A
without defining both these datum levels The datum levels are what
differentiates A from Gibbs energy G

The maximum useful work achievable from a system changing state from
1 to 2 is given by
Wmax = ∆A= -(A2 - Al) = Al - A2
The specific availability, a , i.e. the availability per unit mass is
a = u + pov - Tos
If the value of a were based on unit amount of substance (i.e.
kmol) it would be referred to as the molar availability
The change of specific (or molar) availability is
∆a = a2 - a1 = (u2 + pov2 - Tos2)- (u1 + pov1-Tos1)
= ( h2 + v2(Po-P2) - (h1+ V1(Po – P1)) -To(S2 - S1) 6/10/2017NAPHIS AHAMAD(ME)JIT 31

Availability of a Steady Flow System
Consider a steady flow system and let it be assumed that the flowing
fluid has the following properties and characteristics; Internal energy u,
specific volume v, specific enthalpy h, pressure p, velocity c and
location z
System delivers a work output W units
Normally, P2 &T2 ambient or state dead condition 6/10/2017NAPHIS AHAMAD(ME)JIT 32

Heat Q rejected by the system may be made to run a reversible heat
engine, the output from the engines equal to
=Q – To (S1 – S2)
Maximum available useful work or net work Wnet = Ws + Wengine
Irreversibility
The entropy of a system plus its surroundings (i.e. an isolated system)
can never decrease (2nd law).
• The second law states: Ssystem + Ssurr. = 0
where, = final - initial > 0 irreversible (real world)
=0 reversible (frictionless, ideal) 6/10/2017NAPHIS AHAMAD(ME)JIT 33

Entropy

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