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Second Law of thermodynamics and Entropy
General objective
To understand the concepts of second law of TD and entropy
Specific objectivesUnderstand the concepts of second law of
TD from experiences from day to day lifeDevelop the concept ‘Entropy’ from 2nd
law of TDDefine the concept ‘Entropy Generation’Modify the second law to include ‘entropy’Analyze the mechanisms of entropy
transfer for various processes( heat/work transfer, mass flow)
Compute the ‘entropy generation foe different systems (open, closed)
Need for second law of TD
Y some processes occur ‘NATURALLY’
Why don’t a cold ‘ PEPSI ’ kept outside doesn’t get heated up by absorbing some energy from atmosphere
If you connect two chambers with different gases they get mixed up slowly, why the reverse is not happening ?
What’s the maximum efficiency we can obtain from an engine.
Statements ….. ;-)
KELVIN-PLANK’S STATEMENTNo one can construct a 100%
efficient heat engine
CLAUSIUS STATEMENT You need a refrigerator to further
cool a cold ‘PEPSI’
Clausius inequality
From Carnot theorem…….. For any reversible engine operating
between reservoirs at TH & TL and exchanging heats QH & QL
QH/QL=TH/TL
From carnot theorem, QH/QL=TH/TL
Integrating the equation for a cycle,
A clear violation of ……??!!
Kelvin plank’s statement
Applicable for all processesFor an internally reversible process….
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Consider the cycle shown below composed of two reversible processes A and B.
B
A
2
V
P
1
A cycle composed of two reversible processes.
Apply the Clausius inequality for the cycle made of two internally reversible processes:
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You should find:
Since the quantity (Qnet/T)int rev is independent of the path and must be a property, we call this property the entropy S.
The entropy change occurring during a process is related to the heat transfer and the temperature of the system. The entropy is given the symbol S (kJ/K), and the specific entropy is s (kJ/kgK).
The entropy change during a reversible process, sometimes called an internally reversible process, is defined as
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Consider the cycle 1-A-2-B-1, shown below, where process A is arbitrary that is, it can be either reversible or irreversible, and process B is internally reversible.
The integral along the internally reversible path, process B, is the entropy change S1 –S2. Therefore,
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or
The entropy change during a process dS
dSQ
Tnet
where = holds for the internally reversible process
> holds for the irreversible process
Consider the effect of heat transfer on entropy for the internally reversible case. dS
Q
Tnet
That is,
Q then dS
Q then dS
Q then dS
net
net
net
0 0
0 0
0 0
,
,
,
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From the above, we see that for a reversible, adiabatic process
dS
S S
0
2 1
The reversible, adiabatic process is called an isentropic process.
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•That is, the entropy change of a system during an irreversible process is always greater than , called the entropy transfer. •Some entropy is generated or created during an irreversible process,•This generation is entirely due to the presence of irreversibilities. •The entropy generated during a process is called entropy generation and is denoted as Sgen.
Sgen is always a positive quantity or zero. Its value depends upon the process and thus it is not a property. Sgen is zero for an internally reversible process.
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Now consider an isolated system composed of several subsystems exchanging energy.Since the isolated system has no energy transfer across its system boundary, Applying the definition of entropy to the isolated system
The total entropy change for the isolated system
0isolatedS
Definition of Second Law of Thermodynamics
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The second law, known as the principle of increase of entropy, can also be stated as
The total entropy change of an isolated system during a process always increases or, in the limiting case of a reversible process, remains constant.
The increase in entropy principle can be summarized as follows:
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Some Remarks about Entropy
1. Processes can occur in a certain direction only, not in just any direction, such that Sgen≥0.
2. Entropy is a nonconserved property, and there is no such thing as the conservation of entropy principle. The entropy of the universe is continuously increasing.
3. The performance of engineering systems is degraded by the presence of irreversibilities, and entropy generation is a measure of the magnitudes of the irreversibilities present during that process.
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ENTROPY BALANCE
Energy and entropy balances for a
system.
Entropy Change of a System, ∆Ssystem
When the properties of the system are not uniform
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Mechanisms of Entropy Transfer, Sin and Sout
1 Heat TransferEntropy transfer by heat transfer:
Entropy transfer by work:
Heat transfer is always accompanied by entropy transfer in the amount of Q/T, where T is the boundary temperature.
No entropy accompanies work as it crosses the system boundary. But entropy may be generated within the system as work is dissipated into a less useful form of energy.
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2 Mass FlowEntropy transfer by mass:
Mass contains entropy as well as energy, and thus mass flow into or out of system is always accompanied by energy and entropy transfer.
When the properties of the mass change during the process
Mechanisms of Entropy Transfer, Sin and Sout
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Entropy Generation, Sgen
Mechanisms of entropy transfer for a general system.
Entropy generation outside system boundaries can be accounted
for by writing an entropy balance on an extended
system that includes the
system and its immediate
surroundings.
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Closed Systems
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Control Volumes
The entropy of a substance always increases (or remains constant in the case of a reversible process) as it flows through a single-stream, adiabatic, steady-flow device.
The entropy of a control volume changes as a result of mass flow as well as heat transfer.
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Entropy balance for heat transfer through a wall
Entropy balance for a throttling process
EXAMPLES
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Entropy generation associated with a heat transfer process
Graphical representation of entropy generation during a heat transfer process through a finite temperature difference.
