Second Law of Thermodynamics.

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Lecture 2

• Second Law of Thermodynamics.
• Entropy.

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Second Law of Thermodynamics
Two equivalent statements of the Second Law 1)
"It is impossible for the system to operate in
such a way that sole result is the transfer of
heat from a cold to a hot object." (Clausius
Statement) 2) "It is impossible for a system
that operates in a cycle to generate work while
transferring heat from a single reservoir."
(Kelvin-Planck Statement)
Lets prove that those statements are equivalent
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From C-statement to KP statement.(C ? KP)
Let's prove that if 1 is correct then 2 must be
correct too. Let's assume that contrary to
Clausius Statement it is possible to pump heat
from cold object to a hot one without doing work.
We can illustrate the statement in a following
way
Let's say that amount of heat transferred from
cold bath to hot bath is Q1.
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C ? KP (2)
Now let's add a heat engine to the system such
that amount of heat it absorbs within its cycle
equals Q1, while amount of work done is W and
amount of heat dumped to the cold bath is Q2
Heat exchange with hot bath cancels and our
system is equivalent to
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C ? KP (3)
Heat exchange with hot bath cancels and our
system is equivalent to
So if C Statement is true then KP statement
must be true also. How would we prove KP ?
C?
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Whats next?
So weve shown that C statement and KP
statement of the Second Law are equivalent.
So whats next?
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Whats next?

• Second Law gives us
• defined direction of spontaneous process
• upper limit on anyone's ability to convert heat
  into work
• definition of absolute temperature
• definition of entropy as a new state function
• suggests interesting properties of entropy for
  systems not in the state of equilibrium

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Whats next?
But first we need to define a concept of
reversible process and a special tool
reversible heat engine and well need to examine
properties of this engine
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Reversible process

• A reversible process (or reversible cycle if the
  process is cyclic) is a process that can be
  "reversed" by means of infinitesimal changes in
  some property of the system.
• Due to these infinitesimal changes, the system
  stays at equilibrium throughout the whole
  process.
• In a reversible cycle, the system and its
  surroundings will be exactly the same after each
  cycle.

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Reversible heat engine

• What it does
• on reverse gives back to the surroundings
  whatever it takes on the forward stroke (and
  itself returns to the original state)
• What it does not
• no friction
• no temperature gradients
• no pressure gradients

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Properties of reversible heat engine(Carnot
principles)

• No irreversible heat engine has greater
  efficiency then the reversible engine operating
  between the same thermal reservoirs
• All reversible heat engines working between the
  same heat reservoirs have the same efficiency

Nicolas Léonard Sadi Carnot
1796-1832
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Carnot family
General, Minister of War under Napoleon Formulated
First Law of thermodynamics Made contributions
to geometry
Sadi Carnot
President of France
Minister of Finance President of France
Engineer, chemist discovered uranium ore
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Proof of Carnot principles
Definition (engine efficiency) (useful work
produced) / (heat absorbed) Let's prove
principle 1 using the method of contradiction.
First let's construct the following arrangement
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Proof of Carnot principles
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Proof of Carnot principles
Lets run reversible engine backwards
and get
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Proof of Carnot principles
Lets run reversible engine backwards
and get
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Proof of Carnot principles
Lets run reversible engine backwards
and get
Kelvin-Planck statement
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Proof of Carnot principles
?irrev ?rev
leads to
Therefore any reversible engine will be more
efficient then any irreversible one
impossible
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Proof of Carnot principles
how would we prove principle 2 ? All
reversible heat engines operating between same
heat reservoirs have same efficiency
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What do we have so far?
?max f (TH,TC)
but what is the nature of function f(TH,TC)?
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Absolute temperature
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Absolute temperature
According to Carnot principle 2 efficiency of
engine C is the same as that of D. Well use
that
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Absolute temperature
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Absolute temperature
LHS ? f(T2), so must be RHS i.e. T2 dependence
must cancel!
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Absolute temperature
T2 dependence must cancel. so f() has to be
This way T2 cancels!
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Absolute temperature
So far Lets propose Then we have
(Kelvins definition)
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Absolute temperature(Kelvin Scale)
Heats could be measured by calorimeters number
273.16 can be found by binding 1 K increment to
1oC
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Maximum efficiency
Since max efficiency is (Remember?...
reversible engine is the most efficient)
(sorry) TL is the same as TC L meant low, C
meant cold which is the same in our context
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Entropy
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Entropy
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Entropy
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Entropy
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Entropy
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Entropy
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Maximum entropy principle
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Maximum entropy principle
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Maximum entropy principle
Qadiabatic 0
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Maximum entropy principle
dQadiabatic 0, so
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Maximum entropy principle
In cyclic non-equilibrium adiabatic process new
entropy has to be generated Entropy will reach
maximum at the state of equilibrium