Department of Mechanical Engineering
ME 322 – Mechanical Engineering
Thermodynamics
Lecture 21
Second Law Analysis of Closed Systems
The Laws of the Universe
Conservation of Mass – The Continuity Equation
m  m
i
i
e
e

dmsys
dt
Conservation of Energy – The First Law of Thermodynamics


Vi 2
Ve2
g 
g  dEsys
Q  W   m i  hi 
 zi    m e  he 
 ze  
2 gc gc  e
2 gc gc 
dt
i


The Entropy Balance – The Second Law of Thermodynamics
dS sys
Qk
k T  i mi si  e me se  SP  dt
k
2
Isolated System – First Law
Recall that neither mass or energy cross the boundary of
an isolated system. Therefore,
 Eisol
 Eisol  0
Energy is conserved.
Inside an isolated system, there can be subsystems
interacting with the surroundings. Therefore,
 Eisol   Esys   Esurr  0
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Isolated System – Second Law
Recall that neither mass or energy cross the boundary of
an isolated system. Therefore,
 Sisol
 Sisol  S P ,isol
For real-world
processes the entropy
change of the isolated
system must
increase.
Inside an isolated system, there can be subsystems
interacting with the surroundings. Therefore,
 Sisol   S sys   S surr  S P ,isol
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The Principle of Increase of Entropy
Quote of the Day
Die Energie der Welt ist constant.
Die Entropie der Welt strebt
einem Maximum zu.
Translation …
The energy of the world is
constant. The entropy of the
world tends towards a maximum.
Rudolph Clausius
(1822-1888)
Something to think about …
Is the world, as we know it, an isolated system?
What if we replace the word ‘world’ with ‘universe’?
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The Principle of Increase of Entropy
 Sisol   S sys   S surr  S P ,isol
 S sys May be positive or negative
 S surr Must be big enough to ensure SP > 0
What are several examples where a system experiences a
decrease in entropy?
What is the ‘entropy cost’ to the surroundings for each of
these cases?
6
Gearbox Problem
An operating gearbox has 200 hp at its input shaft while 190 hp
are delivered to the output shaft. The gearbox has a steady
state surface temperature of 140 F.
a) Sketch this system, showing all heat and work transfers
along with their correct sign.
b) Write the 2nd Law for this system. Begin with the general
statement of the 2nd Law and cancel terms that can be
neglected.
c) Determine the entropy production rate. How does this change
with surface temperature?
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Piston-Cylinder Problem (w/Ideal Gas)
Neon undergoes a two-step process in a piston-cylinder assembly.
The first process is isothermal compression from (1 atm, 80 F) to 100 psia.
The second process is reversible and adiabatic expansion back to the
initial pressure (1 atm). The gas constant for Neon is .0984 Btu/lbm-R.
The isochoric heat capacity for Neon is .246 Btu/lbm-R.
a) Sketch this sequence of processes on Pv and Ts diagrams. Show
how to use these diagrams to estimate the sign and relative magnitude
of heat transfer and work transfer for each process.
b) Find the entropy change for each process.
c) Find the final temperature for each process.
d) Find the heat transfer and work transfer for each process.
e) Find the overall heat transfer and work transfer.
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