1. Heat Engines, Entropy and the Second Law of Thermodynamics
Chapter 18
Heat Engines,
Entropy
and the
Second Law of Thermodynamics

2. First Law of Thermodynamics – Review
Review: The First Law is a statement of Conservation of Energy
The Law places no restrictions on the types of energy conversions that can occur
In reality, only certain types of energy conversions are observed to take place
Some events (processes) in one direction are more probable than those in the opposite direction

3. William Thomson, Lord Kelvin
1824 – 1907
Physicist and mathematician
Proposed the use of absolute temperature scale
Now named for him
Work in thermodynamics led to idea that energy cannot spontaneously pass from colder to hotter objects

4. Heat Engine
A heat engine is a device that takes in energy by heat, and, operating in a cycle, expels a fraction of that energy by means of work
A heat engine carries some working substance through a cyclical process

5. Heat Engine, cont.
The working substance absorbs energy by heat from a high temperature energy reservoir (Qh)
Work is done by the engine (Weng)
Energy is expelled by heat to a lower temperature reservoir (Qc)

6. Heat Engine, cont. Since it is a cyclical process, ΔEint = 0
Its initial and final internal energies are the same
Therefore, Qnet = Weng
The work done by the engine equals the net energy absorbed by the engine
The work is equal to the area enclosed by the curve of the PV diagram
If the working substance is a gas

7. Thermal Efficiency of a Heat Engine
Thermal efficiency is defined as the ratio of the net work done by the engine during one cycle to the energy input at the higher temperature
We can think of the efficiency as the ratio of what you gain to what you give

8. More About Efficiency
In practice, all heat engines expel only a fraction of the input energy by mechanical work
Therefore, their efficiency is always less than 100%
To have e = 100%, QC must be 0

9. Second Law: Kelvin-Planck Form
It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work
Means that Qc cannot equal 0
Some Qc must be expelled to the environment
Means that e cannot equal 100%

10. Perfect Heat Engine No energy is expelled to the cold reservoir
It takes in some amount of energy and does an equal amount of work
e = 100%
It is an impossible engine

11. Reversible and Irreversible Processes
A reversible process is one for which the system can be returned to its initial state along the same path
And one for which every point along some path is an equilibrium state
An irreversible process does not meet these requirements
Most natural processes are known to be irreversible
Reversible process are an idealization, but some real processes are good approximations

12. Reversible and Irreversible Processes, cont
A real process that is a good approximation of a reversible one will occur very slowly
The system is always very nearly in an equilibrium state
Adding and removing the grains of sand is an example of a real process that can occur slowly enough to be reversible

13. Reversible and Irreversible Processes, Summary
The reversible process is an idealization
All real processes on Earth are irreversible

14. Sadi Carnot
1796 – 1832
First to show the quantitative relationship between work and heat
Book reviewed importance of the steam engine

15. Carnot Engine A theoretical engine developed by Sadi Carnot
A heat engine operating in an ideal, reversible cycle (now called a Carnot Cycle) between two reservoirs is the most efficient engine possible
This sets an upper limit on the efficiencies of all other engines

16. Work by a Carnot Cycle
The net work done by a working substance taken through the Carnot cycle is the greatest amount of work possible for a given amount of energy supplied to the substance at the upper temperature

17. Carnot Cycle
Overview of the processes in a Carnot Cycle

18. Carnot Cycle, A to B A to B is an isothermal expansion
The gas is placed in contact with the high temperature reservoir, Th
The gas absorbs heat |Qh|
The gas does work WAB in raising the piston

19. Carnot Cycle, B to C B to C is an adiabatic expansion
The base of the cylinder is replaced by a thermally nonconducting wall
No heat enters or leaves the system
The temperature falls from Th to Tc
The gas does work WBC

20. Carnot Cycle, C to D
The gas is placed in contact with the cold temperature reservoir
C to D is an isothermal compression
The gas expels energy QC
Work WCD is done on the gas

21. Carnot Cycle, D to A D to A is an adiabatic compression
The gas is again placed against a thermally nonconducting wall
So no heat is exchanged with the surroundings
The temperature of the gas increases from TC to Th
The work done on the gas is WDA

22. Carnot Cycle, PV Diagram
The work done by the engine is shown by the area enclosed by the curve, Weng
The net work is equal to |Qh| – |Qc|
DEint = 0 for the entire cycle

23. Efficiency of a Carnot Engine
Carnot showed that the efficiency of the engine depends on the temperatures of the reservoirs
Temperatures must be in Kelvins
All Carnot engines operating between the same two temperatures will have the same efficiency

24. Notes About Carnot Efficiency
Efficiency is 0 if Th = Tc
Efficiency is 100% only if Tc = 0 K
Such reservoirs are not available
Efficiency is always less than 100%
The efficiency increases as Tc is lowered and as Th is raised
In most practical cases, Tc is near room temperature, 300 K
So generally Th is raised to increase efficiency

25. Real Engine vs. Carnot Engine
All real engines are less efficient than the Carnot engine because they all operate irreversibly so as to complete a cycle in a brief time interval
In addition, real engines are subject to practical difficulties that decrease efficiency
Friction is an example

26. Heat Pumps and Refrigerators
Heat engines can run in reverse
This is not a natural direction of energy transfer
Must put some energy into a device to do this
Devices that do this are called heat pumps or refrigerators
Examples
A refrigerator is a common type of heat pump
An air conditioner is another example of a heat pump

27. Heat Pump Process Energy is extracted from the cold reservoir, QC
Energy is transferred to the hot reservoir, Qh
Work must be done on the engine, W

28. Coefficient of Performance
The effectiveness of a heat pump is described by a number called the coefficient of performance (COP)
In heating mode, the COP is the ratio of the heat transferred in to the work required

29. COP, Heating Mode COP is similar to efficiency
Qh is typically higher than W
Values of COP are generally greater than 1
It is possible for them to be less than 1
We would like the COP to be as high as possible

30. COP, Carnot in Heating Mode
A Carnot cycle heat engine operating in reverse constitutes an ideal heat pump
It will have the highest possible COP for the temperatures between which it operates

31. COP, Cooling Mode
In cooling mode, you “gain” energy from a cold temperature reservoir
A good refrigerator should have a high COP
Typical values are 5 or 6

32. COP, Carnot in Cooling Mode
The highest possible COP is again the Carnot engine running in reverse
As the difference in temperature approaches zero, the theoretical COP approaches infinity
In practice, COP’s are limited to values below 10

33. Second Law – Clausius Form
Energy does not flow spontaneously by heat from a cold object to a hot object
The Second Law can be stated in multiple ways, all can be shown to be equivalent
The form you should use depends on the application

34. Perfect Heat Pump Takes energy from the cold reservoir
Expels an equal amount of energy to the hot reservoir
No work is done
This is an impossible heat pump

35. The Second Law of Thermodynamics, Summary
Establishes which processes do and which do not occur
Some processes can occur in either direction according to the First Law
They are observed to occur only in one direction
Real processes proceed in a preferred direction
This directionality is governed by the Second Law

36. Entropy
Entropy, S, is a state variable related to the Second Law of Thermodynamics
The importance of entropy grew with the development of statistical mechanics
A main result is isolated systems tend toward disorder and entropy is a natural measure of this disorder

37. Microstates vs. Macrostates
A microstate is a particular configuration of the individual constituents of the system
A macrostate is a description of the conditions from a macroscopic point of view
It makes use of macroscopic variables such as pressure, density, and temperature for gases

38. Microstates vs. Macrostates, cont
For a given macrostate, a number of microstates are possible
The number of microstates associated with a given macrostate is not the same for all macrostates
When all possible macrostates are examined, it is found that the most probable macrostate is that with the largest number of possible microstates

39. Microstates vs. Macrostates, Probabilities
High-probability macrostates are disordered macrostates
Low-probability macrostates are ordered macrostates
All physical processes tend toward more probable macrostates for the system and its surroundings
The more probable macrostate is always one of higher disorder

40. Entropy Entropy is a measure of disorder of a state
Entropy can be defined using macroscopic concepts of heat and temperature
Entropy can also be defined in terms of the number of microstates, W, in a macrostate whose entropy is S
S = kB ln W

41. Entropy and the Second Law
The entropy of the Universe increases in all real processes
This is another statement of the Second Law of Thermodynamics
The change in entropy in an arbitrary reversible process is

42. DS For A Reversible Cycle
DS = 0 for any reversible cycle
In general,
This integral symbol indicates the integral is over a closed path

43. Entropy Changes in Irreversible Processes
To calculate the change in entropy in a real system, remember that entropy depends only on the state of the system
Do not use Q, the actual energy transfer in the process
Distinguish this from Qr, the amount of energy that would have been transferred by heat along a reversible path
Qr is the correct value to use for DS

44. Entropy Changes in Irreversible Processes, cont
In general, the total entropy and therefore the total disorder always increase in an irreversible process
The total entropy of an isolated system undergoes a change that cannot decrease
This is another statement of the Second Law of Thermodynamics

45. Entropy Changes in Irreversible Processes, final
If the process is irreversible, then the total entropy of an isolated system always increases
In a reversible process, the total entropy of an isolated system remains constant
The change in entropy of the Universe must be greater than zero for an irreversible process and equal to zero for a reversible process

46. Heat Death of the Universe
Ultimately, the entropy of the Universe should reach a maximum value
At this value, the Universe will be in a state of uniform temperature and density
All physical, chemical, and biological processes will cease
The state of perfect disorder implies that no energy is available for doing work
This state is called the heat death of the Universe

47. DS in Free Expansion Consider an adiabatic free expansion
The process is neither reversible or quasi-static
W = 0 and Q = 0
Need to find Qr, choose an isothermal process

48. DS in Free Expansion, cont
For an isothermal process, this becomes
Since Vf > Vi, DS is positive
This indicates that both the entropy and the disorder of the gas increase as a result of the irreversible adiabatic expansion

49. Atmosphere as a Heat Engine
The Earth’s atmosphere can be modeled as a heat engine
The energy from the Sun undergoes various processes
Reflected
Absorbed by the air or the surface

50. Energy Balance in the Atmosphere

51. Work Done on the Atmosphere
One process is missing from the previous energy balance
The various processes result in a small amount of work done on the atmosphere
This work appears as the kinetic energy of the prevailing winds in the atmosphere

52. Schematic, Atmosphere as a Heat Engine
The amount of incoming solar energy converted to kinetic energy of the winds is about 0.5%
It is temporarily kinetic energy, eventually radiated into space
As radiation

53. Efficiency of the Atmospheric Heat Engine
The warm reservoir is the surface
The cold reservoir is empty space
The efficiency can be calculated: