1. Second Law of Thermodynamicsq1 q2

2. Reading Hess Tsonis Bohren & Albrecht Wallace and Hobbs Chapter 3
pp 32 – 37
Tsonis
Chapter 5
pp 49 – 70
Bohren & Albrecht
Chapter 4 pp
Wallace and Hobbs
pp 93-97

3. Objectives
Be able to state the Second Law of Thermodynamics in its various forms
Be able to define heat engine
Be able to draw the Carnot cycle and describe the changes in state variables, heat and work throughout the cycle

4. Objectives
Be able to determine whether work is done by or on a system through a Carnot cycle
Be able to define ‘cyclic process’
Be able to define the term ‘reversible process’

5. Objectives
Be able to describe and give examples of natural, reversible, and impossible processes
Be able to calculate the change of entropy of a system

6. First Law of Thermodynamics
“Energy cannot be created or destroyed. It can only be changed from one form into another.”
Rudolf Clausius 1850

7. First Law of Thermodynamics
Conservation of Energy
Says Nothing About Direction of Energy Transfer

8. Second Law of Thermodynamics
Preferred (or Natural) Direction of Energy Transfer
Spontaneous Process
Hot
Cold dQ

9. Second Law of Thermodynamics
‘Un-Natural’ Process
Does not occur spontaneously
Requires energy to transfer heat in opposite direction
Hot dQ
Cold

10. Second Law of Thermodynamics
“Heat passes from a warmer to colder body.”
Rudolf Clausius 1850

11. Second Law of Thermodynamics
Duh....

12. Carnot Cycle Nicolas Leonard Sadi Carnot French engineer and physicist
A Reflection on the Motive Power of Heat (1824)
Cyclic and Reversible Processes

13. Second Law of Thermodynamics
The foundations of the laws of thermodynamics are a result of the steam engine

14. Thomas Newcomen Steam Engine 1765

15. Heat Engine Absorb Heat From Source Performs Mechanical Work
Discards Some Heat At Lower Temperature

16. Carnot Cycle
The atmosphere is a giant heat engine
Hot
Cold dQ

17. Cyclic Process
Sequence of Processes That Leaves A Working Substance In The Same State In Which It Started P V

18. Types of Cycles
Otto Cycle
Internal Combustion Engine

19. Types of Cycles
Diesel Cycle
Internal Combustion Engine

20. Types of Cycles
Rankin Cycle

21. Types of Cycles Carnot Cycle Basis for All Others P q1 q2 T1 T2 V A BD A B C T1 T2 q1 q2 P V

22. Carnot Cycle Heat Engine
Performs work by transferring heat from warm reservoir to colder reservoir D A B C T1 T2 q1 q2 P V
Warm
Cold

23. Types of Cycles Carnot Cycle
Heat Absorbed at Same Temperature as Heat Reservoir D A B C T1 T2 q1 q2 P V
Warm

24. Types of Cycles Carnot Cycle
Heat Rejected at Same Temperature as Cold Reservoir D A B C T1 T2 q1 q2 P V
Warm
Cold

25. Types of Cycles Carnot Cycle
Assumes Warm and Cold Reservoirs Are Unaffected by Heat Transfer
Large Source & Sink D A B C T1 T2 q1 q2 P V
Warm
Cold

26. Carnot Cycle Idealized Heat Engine Operating at maximum efficiency
No system works ‘exactly’ like this
Gives us a foundation for discovery D A B C T1 T2 q1 q2 P V

27. Carnot Cycle Isothermal Expansion Heat Added = Work Done
Volume Increases
Pressure Decreases

28. Change of Internal Energy
Carnot Cycle
Adiabatic Expansion
= Work Done
Volume Increases
Pressure Decrease
Temperature Cools
Change of Internal Energy

29. Carnot Cycle Isothermal Compression Heat Removed = Work Done
Volume Decreases
Pressure Increase

30. Change of Internal Energy
Carnot Cycle
Adiabatic Compression
= Work Done
Volume Decreases
Pressure Increase
Temperature Warms
Change of Internal Energy

31. Carnot Cycle
Adiabat P q1
Adiabat q2 A B T1
Isotherm D T2
Isotherm C V

32. Carnot Cycle Isothermal Expansion Adiabat Q1 Heat Added P q1 AdiabatV
Isothermal Expansion

33. Carnot Cycle Adiabatic Expansion Adiabat cvdT = pdV Cooling P q1
Isotherm D T2
Isotherm C V
Adiabatic Expansion

34. Carnot Cycle Isothermal Compression Adiabat P q1 Adiabat Q2
Heat Removed q2 A B T1
Isotherm D T2
Isotherm C V
Isothermal Compression

35. Carnot Cycle Adiabatic Compression Adiabat cvdT = pdV Warming P q1
Isotherm D T2
Isotherm C V
Adiabatic Compression

36. Carnot Cycle
Mechanical energy (work) is done as a result of heat transfer D A B C T1 T2 q1 q2 P V
Warm
Cold

37. Carnot Cycle What if the cycle is reversed?
Heat Taken From Colder Temperature and Deposited at Warmer Temperature D A B C T1 T2 q1 q2 P V
Warm
Cold

38. Carnot Cycle Refrigerator
Heat Taken From Colder Temperature and Deposited at Warmer Temperature

39. Carnot Cycle Refrigerator
Work is required to transferring heat from cold reservoir to warm reservoir D A B C T1 T2 q1 q2 P V
Warm
Cold

40. Carnot Cycle Alternate Form of Second Law
“Heat cannot of itself pass from a cold to a warm body.” D A B C T1 T2 q1 q2 P V
Warm
Cold

41. Carnot Cycle Reversible Process
each state of the system is in equilibrium
process occurs slow enough
state variables reach equilibrium D A B C T1 T2 q1 q2 P V

42. Carnot Cycle Reversible Process
reversal in direction returns substance & environment to original states D A B C T1 T2 q1 q2 P V

43. Carnot Cycle Cyclic Process
A process in which the Initial State is also the Final State D A B C T1 T2 q1 q2 P V

44. Carnot Cycle Cyclic Process Internal Energy (U) is unchanged P q1 q2B C T1 T2 q1 q2 P V

45. Carnot Cycle Cyclic Process An exact differential
Intergral around a closed path is zero D A B C T1 T2 q1 q2 P V

46. Carnot Cycle Cyclic Process Work done is not an exact differential
Path dependent D A B C T1 T2 q1 q2 P V

47. Carnot Cycle W1 Work done by system during expansion D A B C T1 T2 q1V W1
Work done by system during expansion

48. Carnot Cycle W2 Work done on system during compression P q1 q2 A B T1V
Work done on system during compression

49. Carnot Cycle P V q1 q2 A B DW T1 D T2 C
Net work done by system

50. Carnot Cycle Cyclic Process
Net work done by system is the net heat absorbed D A B C T1 T2 q1 q2 P V

51. Carnot Cycle Net work done by system DW = DQ = Q1 - Q2 q1 P q2 Q1 A BV D A B C T1 T2 q1 q2 Q1 Q2
DW = DQ = Q1 - Q2

52. Carnot Cycle Efficiency of a System
Cannot Convert All Heat Available Into Work P V D A B C T1 T2 q1 q2 Q1 Q2

53. Carnot Cycle Problems Net work done q1 P Path dependent q2 A
Not mathematically “elegant”
Difficult to make quick calcualtions P V D A B C T1 T2 q1 q2
QNet

54. Carnot Cycle
Is there a way to describe the heat change of a system without having to deal with “work done”?
YES!!!!
…but it will take some work!

55. For an adiabatic process
Carnot Cycle
Before we begin...
It can be shown from the First Law & the Ideal Gas Law
Poisson’s Equation
For an adiabatic process
where g = cp/cv

56. Carnot Cycle Lets examine each “leg” of the cycle q1 P q2 Q1 A B T1 DV D A B C T1 T2 q1 q2 Q1 Q2

57. Carnot Cycle From A to B PAVA = PBVB isothermal expansion
temperature is constant (T1) so.. P V q1 q2 Q1 A B T1 T2
PAVA = PBVB

58. Carnot Cycle From A to B isothermal expansion
work done (W1) is heat added (Q1) P V q1 q2 Q1 A B T1 T2

59. Carnot Cycle From A to B heat added (Q1) for 1 mole q1 P q2 Q1 A B T1V q1 q2 Q1 A B T1 T2
Ideal Gas
Law
So...

60. Carnot Cycle From A to B heat added (Q1) for 1 mole q1 P q2 Q1 A B T1V q1 q2 Q1 A B T1 T2

61. Carnot Cycle From B to C PCVgC = PBVgB adiabatic expansion (q2) q1 P

62. Carnot Cycle From C to D isothermal compression
work done (W2) is heat removed (Q2) q1 P q2 T1 D Q2 C T2 V

63. Carnot Cycle From C to D heat removed (Q2) for 1 mole q1 P q2 T1 D Q2
Ideal Gas
Law
So...

64. Carnot Cycle From C to D heat added (Q1) for 1 mole q1 P q2 T1 D Q2 T2V

65. Carnot Cycle From D to A PDVgD = PAVgA adiabatic compression (q2) q1 P

66. Carnot Cycle For the adiabatic processes q1 P q2 A B T1 D T2 CV q1 q2 A B T1 D C T2
Take the ratio
Remember this!! or

67. Carnot Cycle For the isothermal processes q1 P q2 Q1 A B T1 D Q2 T2 CV q1 q2 A Q1 B T1 D Q2 C T2
Take the ratio

68. Carnot Cycle For the isothermal processes q1 P q2 Q1 A B T1 But .... DV q1 q2 A Q1 B T1
But .... D Q2 C T2

69. Carnot Cycle For the cyclic process A lot of work just to say ... q1 PV q1 q2 A Q1 B T1 D Q2 C T2
A lot of work just to say ...

70. Carnot Cycle For a cyclic processV D A B C T1 T2 q1 q2 Q1 Q2
The ratio of the heat absorbed to heat rejected depends only on the initial and final temperature

71. Carnot Cycle
That’s great for steam engines, but what about the atmosphere?

72. Carnot Cycle
Patience, grasshopper!

73. Carnot Cycle Isothermal Process Heat absorbed or released
Amount of heat depends on temperature P V D A B C T1 T2 q1 q2 Q1 Q2

74. Carnot Cycle
But ... P V D A B C T1 T2 q1 q2 Q1 Q2 or
The ratio Q/T is the same regardless of the isotherm chosen

75. Carnot Cycle
The ratio P V D A B C T1 T2 q1 q2 Q1 Q2
is a measure of the difference between the two adiabats.
It is the same for any two adiabats in a cyclic process

76. For a reversible process
Entropy
Difference in entropy between adiabats P V q1 q2 Q1 A B T1 D Q2 C T2
For a reversible process

77. Entropy The path dependent integral no longer depends on path q1 P q2V q1 q2 T1 dQ T2

78. Entropy An integrating factor (T) makes the differential exact P Q1 T1V

79. Entropy For the cyclic & reversible process P Q1 T1 Q2 T2 1st Law V
Ideal Gas Law

80. Entropy
Substitute for a
Integrate

81. Entropy
Over the closed path P V T1 T2 Q1 Q2
So ....

82. Entropy
Function of state
T, P
Not path dependent P V T1 T2 Q1 Q2

83. Entropy
For adiabatic processes P V T1 T2 q1 q2
But ...
So ...

84. Entropy For adiabatic processes No change in entropy Isentropic q1 PV T1 T2 q1 q2

85. Entropy
Potential temperature (q) is conserved for adiabatic processes!
How is potential temperature related to entropy?

86. Entropy
Logarithmically Differentiate

87. Entropy
Wait a second ...
This looks like ...
Let’s combine them!

88. Entropy
Combining equations
Integrate

89. Entropy Meteorologically speaking ...
Entropy depends only on potential temperature!
Dry adiabatic processes are isentropic!

90. Review Second Law of Thermodynamics
It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work, with the system ending in the same state in which it began.

91. Review Second Law of Thermodynamics
It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter body.

92. Second Law of Thermodynamics
No process is possible in which the total entropy decreases, when all systems taking part in the process are included.

93. Types of Processes
Natural (or Irreversible)
Impossible
Reversible

94. Natural (or Irreversible) Process
Processes That Proceed Spontaneously in One Direction But Not The Other
Non-Equilibrium Process
Equilibrium Only At End of Process

95. Natural (or Irreversible) Process
Examples
Conversion of Work to Heat Through Friction
Free Expansion of Gas

96. Natural (or Irreversible) Process
Most Natural Processes Are Irreversible
Analogy – Water Wheel
Water Flows from Higher Elevation to Lower Elevation
Work is Done

97. Natural (or Irreversible) Process
Analogy – Water Wheel
Water Ends Up At A Lower Height
Unable to Perform More Work

98. Natural (or Irreversible) Process
Analogy – Water Wheel
Irreversible
Water Does Not Flow Back Up By Itself

99. Natural (or Irreversible) Process
Similarly, some of the heat is not available to due work T1 T2 q1 q2 P V
Warm
Cold

100. Impossible Process
Violate Second Law
Cannot Occur

101. Impossible Process Examples Free Compression of Air
Conduction in which Cold Object Gets Colder and Warm Object Gets Warmer

102. Reversible Process
System & Surroundings Already Close to Thermodynamic Equilibrium
Changes of State Can Be Reversed Through Infinitesimal Changes

103. Reversible Process System Always in Equilibrium Idealized Concept
Changes Would Never Take Place Initially
Small Changes

104. Entropy Carnot Cycle Idealize Engine Reversible Process
Maximum Efficiency P q1
dQ1 q2 T1
dQ2 T2 V

105. Dry Adiabatic Process Isentropic Reversible No Change in Entropy
Potential Temperature is Constant
Reversible
Substance and Environment return to original condition

106. Entropy Real World Dry Adiabatic Process
Approximation to real world conditions
Not what really happens
Mixing

107. Entropy
A Quantitative Measure of Randomness or Disorder

108. Entropy Example Conversion of Mechanical Energy Into Heat
Increase in Disorder
Random Molecular Motion

109. Entropy In The Atmosphere
Processes Are Not Exactly Dry Adiabatic Process

110. Entropy
Most Natural Processes Are Irreversible

111. Entropy
Would Require More Energy to Return System and Environment to Equilibrium

112. Entropy
This implies an increase in entropy

113. Entropy The entropy of the universe is ever increasing
Conversion from more useful to less useful states