Transcript Part III

The Laws of
Thermodynamics
The Zeroth Law of Thermodynamics
“If two systems are separately in thermal
equilibrium with a third system, they are
in thermal equilibrium with each other.”
This allows the design & the use of
Thermometers!
The First Law of Thermodynamics
Heat absorbed
by the system
Q = ∆Ē + W
Change in the system’s
internal energy
Work done
by the system
For Infinitesimal, Quasi-Static Processes
đQ = dĒ + đW
Total Energy is Conserved
“Energy can neither be
created nor destroyed.
It can only be changed
from one form to another.”
Rudolf Clausius, 1850
• The 1st Law of Thermodynamics is
Conservation of Total Energy!!!!
• It says nothing about
The Direction of Energy Transfer!
(courtesy F. Remer)
The Second Law of Thermodynamics
“The entropy of an isolated system
increases in any irreversible process and is
unaltered in any reversible process.”
• This is sometimes called
The Principle of Increasing Entropy
Change in entropy
of the system
DS  0
• This gives the Preferred (natural)
Direction of Energy Transfer
• This determines whether a process can occur or not.
(courtesy F. Remer)
Historical Comments
• Much early thermodynamics development was
driven by practical considerations.
• For example, building heat engines & refrigerators.
• So, the original statements of the
Second Law of Thermodynamics
may seem different than that just mentioned.
Various Statements of the Second Law
1. “No series of processes is possible whose sole
result is the absorption of heat from a thermal
reservoir and the complete conversion of this
energy to work.” That is
There are no perfect engines!
2. “It will arouse changes while the heat transfers
from a low temperature object to a high
temperature object.”
Rudolf Clausius’
statement of the Second Law.
Strange sounding?
3. “It will arouse other changes
while the heat from the single
thermal source is taken out and is
totally changed into work.”
Lord Kelvin’s (William Thompson’s)
statement of the Second Law.
4. “It is impossible to extract an
amount of heat QH from a hot
reservoir and use it all to do work
W. Some amount of heat QC must
be exhausted to a cold reservoir.”
The Kelvin-Planck
statement of the Second Law.
Heat Engine 
A system that can convert some of the random molecular
energy of heat flow into macroscopic mechanical energy.
QH  HEAT absorbed by a Heat Engine
from a hot body
-W  WORK performed by a Heat Engine
on the surroundings
-QC  HEAT emitted by Heat Engine to a cold body
The Second Law Applied to Heat Engines
Efficiency
= (W/QH) = [(QH - QC)/QH]
A “Heat Engine” That Violates the Second Law
Heat Reservoir
Heat q
Cyclic Machine
Work Output=q
Refrigerator 
A system that can do macroscopic work to extract heat
from a cold body and exhaust it to a hot body, thus
cooling the cold body further.
A system that operates like a Heat Engine in reverse.
QC  HEAT extracted by a Refrigerator from a cold body
W  WORK performed by a Refrigerator
on the surroundings
-QH  HEAT emitted by a Refrigerator to a hot body
The 2nd Law of Thermodynamics
Clausius’ statement for Refrigerators
• “It is not possible for heat to flow
from a colder body to a warmer body
without any work having been done
to accomplish this flow. Energy will
not flow spontaneously from a low
temperature object to a higher
temperature object.”
There are no perfect Refrigerators!
• This statement about refrigerators also applies to air
conditioners and heat pumps which use the same principles.
The Second Law Applied to Refrigerators
Efficiency
= (QC/W) = [(QC)/(QH - QC)]
The 2nd Law of Thermodynamics
can be used to classify
Thermodynamic Processes into
3 Types:
1. Natural Processes
(or Irreversible Processes,
or Spontaneous Processes)
2. Impossible Processes
3. Reversible Processes
We’ll discuss each more thoroughly with examples soon.
(courtesy F. Remer)
The Third Law of Thermodynamics
“It is impossible to reach a temperature
of absolute zero.”
On the Kelvin Temperature Scale,
T=0K
is often referred to as
“Absolute Zero”
Another Statement of The Third Law of
Thermodynamics
“The entropy of a true equilibrium
state of a system at T = 0 K is zero.”
(Strictly speaking, this is true only if the quantum mechanical ground state
is non-degenerate. If it is degenerate,
the entropy at T = 0 K is a small constant, not 0!)
This is Equivalent to:
“It is impossible to reduce the temperature of a
system to T = 0 K using a finite number of
processes.”
Some Popular Versions of
The Laws of Thermodynamics
1st Law: You can’t win.
2nd Law: You can’t break even.
3rd Law: There’s no point in trying.
Other Popular Versions of
The Laws of Thermodynamics
Zeroth Law:
First Law:
Second Law:
Third Law:
Version 1
You must play the game.
You can't win the game.
You can't break even in the game.
You can't quit the game.
Zeroth Law:
First Law:
Second Law:
Third Law:
Version 2
You must play the game.
You can't win the game, you can only break even.
You can only break even at absolute zero.
You can't reach absolute zero.
Zeroth Law:
First Law:
Second Law:
Third Law:
Version 3
You must play the game.
You can't win the game.
You can't break even except on a very cold day.
It never gets that cold!
Zeroth Law:
First Law:
Second Law:
Third Law:
Version 4
There is a game.
You can't win the game.
You must lose the game.
You can't quit the game.
“Murphy's Law of Thermodynamics”
Things get worse under pressure!!
From Statistical Arguments
we’ve seen that a Quantitative Definition of
Entropy is
S  kBln()
kB  Boltzmann’s constant
 = (E)  Number of microstates at a given energy
Spontaneous Processes & Entropy
Spontaneous Processes 
Processes that can proceed with no
outside intervention
Entropy
• In qualitative terms, Entropy can be
viewed as a measure of the
randomness or disorder of the atoms
& molecules in a system.
2nd Law of Thermodynamics
Total Entropy always increases in a
spontaneous process!
So, Microscopic Disorder
also increases in a
spontaneous process!
Spontaneous Processes
Spontaneous Processes 
Processes that can proceed with no
outside intervention.
• Example in the figure: Due to the
2nd Law of Thermodynamics
the gas in container B will
spontaneously effuse into container A.
But, once the gas is in both containers,
it will not
spontaneously effuse back into
container B.
The 2nd Law of Thermodynamics
Processes that are spontaneous
in one direction
are not spontaneous
in the reverse direction.
Example in the figure: Due to the
2nd Law of Thermodynamics
the shiny nail in the top figure will, over a
long time, rust & eventually look as in the
bottom figure. But, if the nail is rusty,
it will not
spontaneously become shiny again!!
• Processes that are spontaneous at one temperature
may be non-spontaneous at other temperatures.
• Example in the figure:
For T > 0C ice will melt spontaneously.
For T < 0C, the reverse process is spontaneous.
Irreversible Processes
Irreversible Processes 
Processes that cannot be undone by exactly reversing the process.
All Spontaneous
Processes are Irreversible.
All Real processes are Irreversible.
Examples of Spontaneous, Irreversible Processes
1. Due to frictional effects, mechanical work changes into heat
automatically.
2. Gas inflates toward vacuum.
3. Heat transfers from a high temperature object to a low
temperature object.
4. Two solutions of different concentrations are put together
and mixed uniformly.
Note!!
The 2nd Law of Thermodynamics says that the
opposite processes of these cannot proceed
automatically. In order to take a system back to it’s
initial state, external work must be done on it.
Spontaneous Processes (changes):
Once the process begins, it proceeds automatically
without the need to do work on the system.
• The opposite of every Spontaneous Process is a
Non-Spontaneous Process
that can only proceed if external work is done on the system.
Reversible Processes
• In a
Reversible Process,
the system undergoes changes such
that the system plus it’s surroundings
can be put back in their original states
by exactly reversing the process.
• In a
Reversible Process,
changes proceed in infinitesimally
small steps, so that the system is
infinitesimally close to equilibrium at
every step. This is obviously an
idealization & can never happen in a
real system!
Another Statement of the 2nd
Law of Thermodynamics
“The entropy of the universe does not change
for Reversible Processes” and also:
“The entropy of the universe increases for
Spontaneous Processes” “You can’t break even”.
For Reversible (ideal) Processes:
For Irreversible (real, spontaneous) Processes:
Still Another Statement of the
2nd Law of Thermodynamics
“In any spontaneous process, there is
always an increase in the entropy of the
universe.”
The Total Entropy S of the Universe
has the property that, for any process,
∆S ≥ 0.
More Examples of Spontaneous Processes
Free Expansion of a Gas
• The container on the right is filled with gas. The
container on the left is vacuum. The valve between them
is closed. Now, imagine that the valve is opened.
Vacuum
Valve
Closed
Gas
(courtesy F. Remer)
Free Expansion of a Gas
• After the valve is opened, for some time, it is no longer an
equilibrium situation. The 2nd Law says the molecules on the right
will flow to the left. After a sufficient time, a new equilibrium is
reached & the molecules are uniformly distributed between the 2
containers.
The Entropy Increases!!!!
After some time,
there is a new
Equilibrium
Gas
Valve
Open
Gas
(courtesy F. Remer)
Thermal Conduction
• A hot object (red) is brought into thermal contact with a
colder object (blue). The 2nd Law says that heat đQ will
flow from the hot object to the colder object.
Hot
đQ
Cold
(courtesy F. Remer)
• After the 2 objects are brought into thermal contact, for some time,
by the 2nd Law, heat đQ flows from the hot object to the colder
object. During that time, it is no longer an equilibrium situation.
After a sufficient time, a new equilibrium is reached & the 2
objects are at the same temperature.
The Entropy Increases!!!!
Warm
After some time,
there is a new
Equilibrium
(courtesy F. Remer)
Mechanical Energy to Internal Energy Conversion
• Consider a ball of mass m. It’s Mechanical Energy is defined as
E = KE + PE. KE = Kinetic Energy, PE = Potential Energy.
• For conservative forces, E is conserved (a constant).
• Drop the ball from rest at a height h above the ground.
Initially,
E = PE = mgh
Just before hitting
the ground,
h
Conservation of
Mechanical Energy
tells us that
mgh = (½)mv2
E = KE = (½)mv2
Mechanical Energy E
is conserved!
(courtesy F. Remer)
• At the bottom of it’s fall, the ball collides with the ground & bounces upward. If
it has an Elastic Collision with the ground, by definition, right after it has
started up, its mechanical & kinetic energies would be the same as just
before it hit:
E = (½)mv2 = mgh
• In reality, the Collision will be Inelastic. So, the initial upward
kinetic energy, KE', will be less than KE just before it hit.
Just before hitting
the ground,
KE = (½)mv2.
The collision is Inelastic,
so right after it bounces,
its kinetic energy is
KE' < KE.
Where did the lost KE go? It is converted to heat, which changes the
internal energy Ē of the ball. As a result, the ball heats up!!
(courtesy F. Remer)
The ball’s collision with the ground is inelastic, so it loses some
kinetic energy:
KE' < KE. The lost kinetic energy is
converted to heat, which changes the ball’s internal energy Ē.
So, the ball gets warmer!!
In Ch. 4, we’ll show that, for an infinitesimal, quasi-static process
in which an object heats up, changing its temperature by an amount
dT, it’s internal energy change is
dĒ = mcVdT
m ≡ ball’s mass & cV ≡ specific heat at constant volume
KE = (½)mv2
KE' < KE
The change in the ball’s internal energy is
dĒ = mcVdT
(courtesy F. Remer)
Multiple Bounces of the ball
 Multiple Inelastic Collisions with the ground.
When it finally comes to rest after several bounces,
it may be MUCH warmer than when it was dropped!
The ball loses more KE on
each bounce & it eventually
stops on the ground. Thus,
after sufficient time, it tends
towards Equilibrium
The more bounces the ball
has, the warmer it gets!
The Ball’s Entropy Increases!!!!
(courtesy F. Remer)
Brief Discussion of
“Impossible Processes” 
• Processes which are
allowed by the 1st Law of Thermodynamics
but which Cannot Occur Naturally
because they would violate the 2nd Law of
Thermodynamics.
• Any process which would take a system from an equilibrium
state to a non-equilibrium state without work being done on
the system would violate the 2nd Law of Thermodynamics
& thus would be an Impossible Process!
(courtesy F. Remer)
Examples of Impossible Processes
• Example 1: “Free Compression” of a Gas!
Initially, the valve is open
& gas molecules are
uniformly distributed
in the 2 containers.
Gas
Valve
Open
Gas
After some time, all gas
molecules are gathered in
the right container &
the left container is empty.
The Entropy
Decreases!!
Vacuum
Valve
Open
Gas
(courtesy F. Remer)
Thermal Conduction
Initially, an
object is warm.
Warm
After some time,
the left side is hot
& the right side
is cold .
Hot
Cold
The Entropy
Decreases!!
(courtesy F. Remer)
Conversion of Internal Energy to
Mechanical Energy
Initially, a ball is
on the ground
& is hot.
Hot
After some time, the ball
Warm
begins to move upward
with kinetic energy
KE = (½) mv2
& it cools down!
The Entropy
Decreases!!
(courtesy F. Remer)
Impossible Processes
Cannot occur without the input of work
đW
(courtesy F. Remer)
• In such a process, the System’s Entropy Decreases, but the
Total Entropy of the System + Environment Increases
Environment
Decrease
in Entropy
đW
Increase
in Entropy
(courtesy F. Remer)