Transcript 1. Lecture 28 - Snow College

Entropy Balance
Entropy Balance
• Sin – Sout + Sgen = ΔSsystem
• ΔSsystem = Sfinal – Sinitial
• ΔSsystem = 0 if the state of the
system does not change.
–example: steady-flow devices.
Energy and
entropy balances.
Entropy Transfer, Sin and Sout
• By heat transfer
–the only method of entropy
transfer for a closed system.
Heat transfer always results in entropy transfer of Q/Tb.
If temperature of the
boundary is not constant,
then need to integrate or
sum.
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.
Entropy is generated in
the system by friction.
However, state of system
changes so entropy
changes. How?
Entropy Transfer, Sin and Sout
• By mass flow
–only for an open system.
–Smass = ms
Mass contains entropy as well as energy so produces both
entropy and energy transfer.
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.
When evaluating the
entropy transfer
between an extended
system and its
surroundings,
boundary temp is
environment temp.
Entropy Balance for Closed Systems
• No entropy transfer from mass.
– ΣQk/Tk + Sgen = S2 – S1
• If adiabatic, Sgen = S2 – S1
• For system and surroundings,
(an adiabatic system)
– Sgen = ΔSsystem + ΔSsurroundings
• Should start from the general
form and “whittle it down”.
Entropy Balance for Control Volumes
• Again, should start with general
entropy balance equation and
“whittle it down”.
• ΣQk/Tk + Σmisi – Σmese + Sgen =
(S2 – S1)system
• If a steady-flow device:
– ΣQk/Tk + Σmisi – Σmese + Sgen = 0
Example 6-17 Entropy generation in a wall and in its surroundings
First take wall as system. Entropy balance is:
ΣQk/Tk + Σmisi – Σmese + 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 ΔT.
Example 6-18 Entropy Generation Through a Throttling Valve
Take the throttling valve as system. Entropy balance is:
ΣQk/Tk + Σmisi – Σmese + Sgen = (S2 – S1)system
Assumptions?
From energy balance: if Q = 0 and W = 0, then h2 = h1.
sgen = (s2 – s1) = .3691 kJ/kg∙K
The sgen is caused
by unrestrained
expansion.
Example 6-19 A Hot Block in a Lake
ΔS of the iron?
ΔSiron = mCavln(T2/T1) = -12.65 kJ/K
ΔS of the lake?
ΔSlake = Qlake/Tlake = 16.97 kJ/K
Total Sgen?
Sgen = ΔSiron + ΔSlake = 4.32 kJ/K
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 ΔS of the system?
How do we get the total Sgen
for this process?
System?
Where is the entropy generated?
How can a wall be 100°C on one
side and 25°C on the other?