1. Spontaneous (Irreversible) Processes & The 2nd Law of Thermodynamics

2. Quantitatively Defined Entropy: S  kBln()
From Statistical Arguments we’ve
Quantitatively Defined
Entropy: S  kBln()
kB  Boltzmann’s constant
  (E)  Number of Microstates at a Given Energy

3. Entropy Disorder is a measure of the amount of in a system.
We’ve also discussed
the fact that
Entropy
is a measure of
the amount of
Disorder
in a system.

4. Spontaneous Processes & Entropy
Processes that can proceed with no outside intervention.
Entropy can be viewed as a measure of randomness or disorder in the atoms & molecules in a system.
The 2nd Law of Thermodynamics says that
Total Entropy always increases in a spontaneous process!
So, Microscopic Disorder also
always increases in a spontaneous process!

5. Entropy, S
A Measure of Disorder
Ssolid  Sliquid  Sgas

6. Increasing Entropy
Ssolid  Sliquid  Sgas

7. Spontaneous Processes
Processes that can proceed with no outside intervention.
Example in the figure:
Due to the
2nd Law of Thermodynamics,
when the valve is opened, the gas in container B will spontaneously diffuse into container A.
But, once it is in both containers, it will never spontaneously diffuse back into container B.

8. Spontaneous Processes

9. The 2nd Law of Thermodynamics
Processes that are spontaneous in one direction aren’t spontaneous in the reverse direction.
Example in the figure: Due to the
2nd Law of Thermodynamics
the shiny nail at the top will, over a long time, rust & eventually look as at the bottom. But (obviously), if the nail is rusty,
it will not ever
spontaneously become shiny again!!

10. Example in the figure: For T > 0C the ice will melt spontaneously.
Processes that are spontaneous at one temperature may be non-spontaneous at other temperatures.
Example in the figure:
For T > 0C the ice will melt spontaneously.
For T < 0C, the reverse process is spontaneous.

11. Irreversible Processes
Processes that cannot be undone by exactly reversing the process.
All Spontaneous Processes are Irreversible.
All Real processes are Irreversible.

12. Spontaneous Processes:
Always occur on their own, without outside intervention.
Always have a definite direction.
The reverse process is never spontaneous.
Temperature can have an impact on spontaneity.
Examples:
Ice melting or forming
Hot metal cooling at room temperature.

13. Whenever a chemical system is in equilibrium, a reaction can go reversibly to reactants or products.
(Example: water  water vapor at 100 º C).
In a Spontaneous Process, the path between reactants and products is
irreversible.
Discuss the idea that at a constant temperature of 100 degrees Celsius liquid water molecules evaporate as gaseous water molecules are recaptured by the liquid into liquid form. (They are in equilibrium).

14. The reverse of a spontaneous process is
not spontaneous.
“Scrambled eggs
don’t unscramble!”
Discuss the idea that at a constant temperature of 100 degrees Celsius liquid water molecules evaporate as gaseous water molecules are recaptured by the liquid into liquid form. (They are in equilibrium).

15. Spontaneous, Irreversible Processes: More Examples
1. Due to friction, mechanical work
changes into heat automatically.
2. Gas inflates toward vacuum.
Note!! The 2nd Law of Thermo says
that the opposite processes of these
can’t proceed automatically. To take
a system back to it’s initial state,
External work must be done on it.

16. Spontaneous, Irreversible Processes: More Examples
3. Heat transfers from a high temperature
object to a low temperature object.
4. 2 solutions of different concentrations
are put together and mixed uniformly.
Note!! The 2nd Law of Thermo says
that the opposite processes of these
can’t proceed automatically. To take
a system back to it’s initial state,
External work must be done on it.

17. Non-Spontaneous Process
Spontaneous Processes (Changes):
Once such a 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.

18. Reversible Processes (Idealizations!)
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 clearly an
idealization & can never happen in a real system!

19. Other Statements 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:

20. Still Other Statements of the 2nd Law of Thermodynamics
1. “In any spontaneous process, there is
always an increase in the entropy of
the universe.”

21. Still Other Statements of the 2nd Law of Thermodynamics
1. “In any spontaneous process,
there is always an increase in the
entropy of the universe.” Or
2. “The Total Entropy S of the
Universe has the property that, for
any spontaneous process
∆S ≥ 0”.

22. Example: Entropy of the Universe Increases
1200 J of heat flows
spontaneously through a
copper rod from a hot
reservoir at TH = 650 K to a
cold reservoir at TC = 350 K.
Calculate the amount by which this
irreversible process changes the entropy of the
universe. (Assuming no other changes occur).

23. Any irreversible process increases the entropy of the universe.
Solution
The 2nd Law for a system interacting with a
heat reservoir is: + +
Any irreversible process increases the entropy of the universe.

24. 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.
Valve
Closed
Gas
Vacuum

25.  The Entropy Increases!!
After the valve opens, for some time, it is no longer an equilibrium situation. The 2nd Law says molecules on the right will flow to the left. After a time, a new equilibrium is reached & molecules are uniformly distributed between the 2 containers.
 The Entropy Increases!!
After some time,
there is a new
Equilibrium
Valve
Opened
Gas
Gas

26. 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
Cold đQ

27.  The Entropy Increases!!
After the objects are in thermal contact, for some time, by the 2nd Law, heat đQ flows from the hot object to the cold object. During that time, it isn’t an equilibrium situation. After a 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

28. Mechanical Energy to Internal Energy Conversion
Consider a ball of mass m. It’s Mechanical Energy is:
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 h
Conservation of Mechanical Energy
tells us that
mgh = (½)mv2
Just before hitting
the ground,
E = KE = (½)mv2
Mechanical Energy
E is conserved!

29. Just before hitting the
At the bottom of it’s fall, the ball collides with the ground & bounces upward. If it is 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 from the bounce, KE', will be less than KE just before it hit.
The collision is Inelastic, so right after it bounces, its kinetic energy is
KE' < KE.
Just before hitting the
ground,
KE = (½)mv2

30. As a result, the ball heats up!!
E = (½)mv2 = mgh
The Collision is will be Inelastic. So, the initial upward kinetic energy from the bounce, KE', will be less than KE just before it hit.
The collision is Inelastic, so right after it bounces, its kinetic energy is
KE' < KE.
Just before hitting the
ground,
KE = (½)mv2
Where did the “lost” KE go? It is converted to heat,
which changes the internal energy Ē of the ball (1st Law!).
As a result, the ball heats up!!

31. So, the ball gets warmer!! KE' < KE KE = (½)mv2
The ball’s has an inelastic collision with the ground, 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 quasi-static process in which an object heats up, changing its temperature by an amount T, it’s internal energy change is Ē = mcVT
so the ball heats up! m ≡ ball mass cV ≡ specific heat at constant volume.
KE' < KE
KE = (½)mv2

32. It tends towards Equilibrium The Ball’s Entropy Increases!!
With Multiple Bounces of the ball, there will be 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!!

33. Irreversible (Spontaneous) Processes
An object can slide down an incline if friction is overcome.
But it can’t spontaneously move up the incline of its own accord. The conversion of mechanical energy to thermal energy by friction as it slides is irreversible.
In the figure, an ice cube at T = 0 C sits for some time, gradually melting. Eventually, only a puddle of water will remain.

34. More Examples of Spontaneous Processes
Spontaneous processes occur in a system left to itself.
No action from outside the system is necessary to bring
the change about.

35. More Examples of Spontaneous Processes
Spontaneous processes occur in a system left to
itself. No action from outside the system is
necessary to bring the change about.
Example: Dissolving a Solid in
a Liquid (like salt in water)
Ions have more entropy (more states) than the water,
But, some water molecules have less entropy (they’re grouped around ions). There must be an overall increase in entropy.

36. More Examples of Spontaneous Processes how can we account for this?
Spontaneous processes occur in
systems left to themselves. No action
from outside the system is necessary to
cause the change.
Question: Water put into a freezer spontaneously turns to ice. (So, the water entropy decreases!)
Entropy always increases, so,
how can we account for this?

37. Doesn’t this violate the 2nd Law of Thermo?
Question: Water put into a freezer spontaneously turns to ice. (So, the water entropy decreases!) Why?
Doesn’t this violate the 2nd Law of Thermo?

38. Question: Water put into a freezer spontaneously turns to ice
Question: Water put into a freezer spontaneously turns to ice. (So, the water entropy decreases!) Why?
Doesn’t this violate the 2nd Law of Thermo?
Answers
The compressor does work on the ice + freezer.
This causes evaporation & condensation of the refrigerant. This also causes warming of the air around the container
As a result of these effects, the entropy of the universe will increase.

39. Some Processes That Lead to an (Spontaneous Processes)
Increase in Entropy
(Spontaneous Processes)
1. Melting of a solid.
2. Dissolving of a solid in a solution.
3. A solid or a liquid becomes a gas.
4. The temperature of a substance increases.
5. A chemical reaction produces more molecules.

40. “Impossible Processes” Allowed by the 1st Law of Thermo
FYI: Brief Discussion of
“Impossible Processes”
Impossible Processes are those which would be
Allowed by the 1st Law of Thermo
but which Can’t Occur Naturally because
they would violate the 2nd Law of Thermo.

41. Allowed by the 1st Law of Thermo
Brief Discussion of “Impossible Processes”
Impossible Processes are those which would be
Allowed by the 1st Law of Thermo
but which Can’t Occur Naturally because
they would violate the 2nd Law of Thermo.
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 & thus would be an “Impossible Process”!

42. 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.
Valve
Open
Gas
Gas

43. 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.
Valve
Open
After some time, all gas molecules are gathered in the right container & the left container is empty.
Gas
Gas
The Entropy
Decreases!
Vacuum
Gas
Valve
Open

44. Thermal Conduction
Initially,
An object is warm.
Warm

45. So, the Entropy Decreases!!
Thermal Conduction
Initially,
An object is warm.
Warm
After some time,
The left side is hot & the right side is cold!!
Hot
Cold
So, the Entropy Decreases!!

46. Conversion of Internal Energy to Mechanical Energy
Initially, a ball is on the ground & is hot.
Hot

47. Conversion of Internal Energy to Mechanical Energy
Initially, a ball is on the ground & is hot.
Hot
After some time, the ball begins to move upward with kinetic energy
KE = (½) mv2
& it cools down!
Warm
The Entropy
Decreases!

48. “Impossible Processes” Cannot occur without the input of work

49. In such a process, the System’s Entropy Decreases, but the Total Entropy of the System + Environment Increases
Decrease
in Entropy
Environment đW
Increase
in Entropy

50. FYI: Very Brief Discussion: “Perpetual Motion”
We’ve said, “Impossible Processes” are processes which are
Allowed by the 1st Law of Thermo but which Can’t Occur Naturally because they would violate the 2nd Law of Thermo.

51. FYI: Very Brief Discussion: “Perpetual Motion”
We’ve said, “Impossible Processes” are processes which are
Allowed by the 1st Law of Thermo but which Can’t Occur Naturally because they would violate the 2nd Law of Thermo.
Any process which takes a system from an equilibrium state to a non-equilibrium state without work being done on the system
Would violate the 2nd Law of Thermo &
thus Would be an Impossible Process!

52. “Impossible Processes” are processes which are
Allowed by the 1st Law of Thermo but which Can’t Occur Naturally because they would violate the 2nd Law of Thermo.
As examples which we sometimes hear about, the so-called
“Perpetual Motion” or “Free Energy” machines rely on such “Impossible Processes” & thus are
Always Bogus!

53. What is “Perpetual Motion”?
That term describes hypothetical machines that
operate or produce useful work indefinitely &,
more generally, hypothetical machines that
produce more work or energy than they use.
There is an undisputed scientific consensus that
Perpetual motion would violate either the 1st Law or the 2nd Law of Thermodynamics, or both!
Such machines rely on “Impossible Processes” & thus are
Always Bogus!

54. “Perpetual Motion”
Describes a theoretical machine that, without any losses due to friction or other forms of dissipation of energy, would continue to operate indefinitely at the same rate without any external energy being applied to it.
Machines which comply with both the 1st &
2nd Laws of Thermodynamics but access
energy from obscure sources are also sometimes
referred to as “Perpetual Motion” machines,
though they do not meet the standard criteria for
the name.

55. “Perpetual Motion Machines”
& the US Patent & Trademark Office
For over 100+ years now, the US PTO has had a standing rule:
If a patent application is filed which claims to be about a “Perpetual Motion Machine” or a “Free Energy Machine”, etc., it will be rejected without further review.

56. Evidence: Amazon Search: “Free Energy"

57. Brief Overview: Classification of “Perpetual Motion” Machines!
1. “Perpetual Motion” Machine of the 1st Kind 2. “Perpetual Motion” Machine of the 2nd Kind 3. “Perpetual Motion” Machine of the 3rd Kind
What is the project about?
Define the goal of this project
Is it similar to projects in the past or is it a new effort?
Define the scope of this project
Is it an independent project or is it related to other projects?
* Note that this slide is not necessary for weekly status meetings

58. The 1st Kind
A “perpetual motion” machine of the first kind produces work without the input of energy.
It thus violates the 1st Law of Thermodynamics: the Law of Conservation of Energy.
The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over.
A consequence of this law is that energy can neither be created nor destroyed: it can only be transformed from one state to another. So,
It is clearly impossible for a machine to do work indefinitely without consuming energy.
* If any of these issues caused a schedule delay or need to be discussed further, include details in next slide.

59. However, it does violate the 2nd Law of Thermo!
The 2nd Kind
A “perpetual motion” machine of the 2nd kind is a machine which spontaneously converts thermal energy into mechanical work.
When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy.
However, it does violate the 2nd Law of Thermo!
The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.

60. the Complete Elimination of Friction
The 3rd Kind
A “perpetual motion” machine of the 3rd kind is a machine which relies on
the Complete Elimination of Friction
& other dissipative forces, to maintain motion forever.
Technically, it is not so much an energy generating machine so much as a machine that operates without consuming energy. It is not possible to move with zero friction, so although low friction devices are real, zero friction devices are not.ch as an energy storage device.