Entropy Balance

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Entropy Balance
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Entropy Balance

• Sin Sout Sgen ?Ssystem
• ?Ssystem Sfinal Sinitial
• ?Ssystem 0 if the state of the system does not
  change.
• example steady-flow devices.

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Energy and entropy balances.
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Entropy Transfer, Sin and Sout

• By heat transfer
• the only method of entropy transfer for a closed
  system.

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Heat transfer always results in entropy transfer
of Q/Tb.
If temperature of the boundary is not
constant, then need to integrate or sum.
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Entropy Transfer, Sin and Sout

• By heat transfer
• the only method of entropy transfer for a closed
  system.
• If two systems are in contact, -Sout1 Sin2
  since there is no boundary.
• By work
• Swork 0
• Can be used to define the difference between work
  and heat transfer.

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Entropy is generated in the system by friction.
However, state of system changes so entropy
changes. How?
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Entropy Transfer, Sin and Sout

• By mass flow
• only for an open system.
• Smass ms

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Mass contains entropy as well as energy so
produces both entropy and energy transfer.
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Entropy Generation, Sgen

• Sgen is a measure of the entropy created by
  irreversibilities.
• Sgen is zero only for reversible processes.
• so for reversible processes, the entropy balance
  is like the energy balance.
• Sgen is withing the system boundary only.
• so if Sgen 0 then process is internally
  reversible but maybe not externally reversible.
• For total Sgen must look at system and its
  immediate surroundings.

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When evaluating the entropy transfer between an
extended system and its surroundings, boundary
temp is environment temp.
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Entropy Balance for Closed Systems

• No entropy transfer from mass.
• SQk/Tk Sgen S2 S1
• If adiabatic, Sgen S2 S1
• For system and surroundings, (an adiabatic
  system)
• Sgen ?Ssystem ?Ssurroundings
• Should start from the general form and whittle
  it down.

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Entropy Balance for Control Volumes

• Again, should start with general entropy balance
  equation and whittle it down.
• SQk/Tk Smisi Smese Sgen (S2 S1)system
• If a steady-flow device
• SQk/Tk Smisi Smese Sgen 0

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Example 6-17 Entropy generation in a wall and in
its surroundings
First take wall as system. Entropy balance is
SQk/Tk Smisi Smese Sgen (S2 S1)system
Sgen 1035 W/278 K 1035 W/293 K .191 W/K
Next take wall and surroundings as system. How
does our entropy balance change?
Just different temperatures to divide by.
Sgen,total .341 W/K
The sgen is due to heat transfer through a ?T.
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Example 6-18 Entropy Generation Through a
Throttling Valve
Take the throttling valve as system. Entropy
balance is
Assumptions?
SQk/Tk Smisi Smese Sgen (S2 S1)system
From energy balance if Q 0 and W 0, then h2
h1.
sgen (s2 s1) .3691 kJ/kgK
The sgen is caused by unrestrained expansion.
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Example 6-19 A Hot Block in a Lake
?Siron mCavln(T2/T1) -12.65 kJ/K
?S of the iron?
?S of the lake?
?Slake Qlake/Tlake 16.97 kJ/K
Total Sgen?
Sgen ?Siron ?Slake 4.32 kJ/K
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Example 6-21 Entropy Generation Associated with
Heat Transfer
What do we take as a system? What are our
assumptions?
With the water as our system, isothermal,
internally reversible.. What is Sgen? What is ?S
of the system?
How do we get the total Sgen for this
process? System? Where is the entropy
generated? How can a wall be 100C on one side
and 25C on the other?
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