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lesson 16
VI. Entropy
A. Introduction
1. The first law:
energy cannot be created or destroyed
2. The second law:
certain processes do occur and certain
processes don’t
3. The magic vortex tube.
Will it work or won’t it
?
Magic Vortex Tube
Compressed air
2 kg at 4 atm, 300 K
Hot air
1 kg at 1 atm,
333 K
Cold air
1 kg at 1 atm
273 K
We need a
quantitative
answer.
This suggests that we are
looking for a property (like T, P, u, or V).
How can we find
such a property?
lesson 16
VI. Entropy
B. The Clausius Inequality
Rev. Heat
Engine
T
H
T
L
Q
L
Q
H
W
out,net
For a reversible heat engine, (616), is
HL
rev
QQ
Q
or
0
TT
T
δ
=
=
∫
v
For an irreversible heat engine, with Q
H
constant,
irrev
L,irrev
L,rev
Q
Q
Q
or
or
0
T
><
<
∫
v
In general, we have the Clausius inequality,
Q
0
T
≤
∫
v
(71)
H
L
H
L
T
T
Q
Q
=
and
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lesson 16
VI. Entropy
C. A New Property Called Entropy
The equality in (71) holds for a reversible process, the inequality
for an irreversible one.
Q
0
T
δ
≤
∫
v
(71)
We know that the cyclic integral of a property is zero.
Clausius
recognized that the equality
in (71) implies the existence of a new
property, entropy, which we will give the symbol S.
rev
Q
0o
r
dS 0
T
==
∫∫
vv
(74)
⎟
⎠
⎞
⎜
⎝
⎛
=
K
kJ
T
Q
dS
rev
and
Equation 74 can also be written as
rev
Q
dS
kJ
dt
T
s K
⎛⎞
=
⎜⎟
⎝⎠
±
lesson 16
VI. Entropy
Equation 74 can be used to calculate changes in entropy for an
internally reversible, isothermal heat transfer process.
As previously
noted, isothermal heat transfer processes are internally reversible
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This note was uploaded on 09/04/2009 for the course CHEM 2300 taught by Professor Thermo during the Summer '08 term at University of Utah.
 Summer '08
 thermo

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