1. The Laws of Thermodynamics
The laws that govern the processes in which energy is transferred as heat and as work.

2. Zeroth Law of Thermodynamics
Zeroth: Two systems are at thermal equilibrium if they have the same temperature. The significant consequence of the Zeroth Law is that, when a hotter object and a colder object are placed in contact with one another, heat will flow from the hotter object to the colder object until they are in thermal equilibrium.

3. First Law of Thermodynamics
The First Law of Thermodynamics tells us that the internal energy of a system can be increased by adding energy to the system

4. First Law, cont. Energy transfers occur due to
By doing work
Requires a macroscopic displacement of an object through the application of a force
By heat
Occurs through the random molecular collisions
Both result in a change in the internal energy, DU, of the system

5. First Law, Equation
If a system undergoes a change from an initial state to a final state, then DU = Uf – Ui DU is the change in internal energy
DU = Q + W
Q is the energy transferred to the system by heat
W is the work done on the system

6. Sign Convention ΔU = Q + W +Q when heat is added to the system.
- Q when heat is lost from the system.
+W when work is done on the system.
- W when work is done by the system.
Disagreement in Physics community as to how to define the Work Term

7. Notes About Work
Positive work increases the internal energy of the system
Negative work decreases the internal energy of the system
This is consistent with the definition of mechanical work

8. Results of DU
Changes in the internal energy result in changes in the measurable macroscopic variables of the system
These include
Pressure
Temperature
Volume

9. Work in Thermodynamic Processes – Assumptions
Dealing with a gas
Assumed to be in thermodynamic equilibrium
Every part of the gas is at the same temperature
Every part of the gas is at the same pressure
Ideal gas law applies

10. Work in a Gas Cylinder
The gas is contained in a cylinder with a moveable piston
The gas occupies a volume V and exerts pressure P on the walls of the cylinder and on the piston

11. Work in a Gas Cylinder, cont.
A force is applied to slowly compress the gas
The compression is slow enough for all the system to remain essentially in thermal equilibrium
W = - P ∆V
This is the work done on the gas

12. More about Work on a Gas Cylinder
When the gas is compressed
∆V is negative
The work done on the gas is positive
When the gas is allowed to expand
∆V is positive
The work done on the gas is negative
When the volume remains constant
No work is done on the gas

13. First Law Question ΔU = Q + W
In a thermodynamic process, a system absorbs 450 kJ of heat and does 87 kJ of work on its surroundings. By what amount did the system’s internal energy change?
ΔU = Q + W

14. First Law Question ΔU = Q + W
In a thermodynamic process, a system absorbs 450 kJ of heat and does 87 kJ of work on its surroundings. By what amount did the system’s internal energy change?
ΔU = Q + W
Note that the work done by the system ON the surroundings is negative.

15. First Law in a “Nutshell”
Here is a diagram of a generic thermodynamic process.
A system has an initial internal energy.
Heat (Q): can be added to the system, or taken away from the system or there may be no heat transfer.
Work (W): may be done on the system or the system may do work or there may be no work involved at all.

16. For everything we are about to do…
For everything we are about to do…. Always keep in mind the Ideal Gas Law…
PV = nRT

17. The 4 “`Processes”
Isothermal Process – thermodynamic process in which the temperature of the system remains constant.
Occurs often in heat reservoirs (surrounds can supply or soak up excess heat)
Adiabatic Process – thermodynamic process in which no heat is exchanged between the system and its environment.
Occurs rapidly or when well insulated (think a thermos!)
Isobaric Process – thermodynamic process in which the pressure of the system remains constant.
Isochoric Process – thermodynamic process in which the volume of the system remains constant.

18. Isolated System
An isolated system does not interact with its surroundings
No energy transfer takes place and no work is done
Therefore, the internal energy of the isolated system remains constant

19. Cyclic Processes
A cyclic process is one in which the process originates and ends at the same state
Uf = Ui and Q = -W
The net work done per cycle by the gas is equal to the area enclosed by the path representing the process on a PV diagram

20. For the following P vs. V diagram… determine which of the Special Cases applies
Isobaric: pressure is constant
∆𝑼=𝑸+𝑾
W = PΔV
Work can be done if the volume of the system undergoes a change. P V
How could you have a situation where volume increases and Pressure stays constant? T increases or n increases

21. For the following P vs. V diagram… determine which of the Special Cases applies
Isochoric: Volume is constant (taking up the same space)
How does the 1st Law Equation change during an Isochoric process?
In this type of process, the volume stays constant. This means that ΔV is zero. If ΔV is zero, then the work must also be zero. B. P V
How could you have a situation where volume increases and Pressure stays constant? T increases or n increases

22. For the following P vs. V diagram is an Adiabatic Process
Adiabatic Process: no heat is exchanged between the system an its environment
How does the 1st Law Equation change during an Adiabatic process?
ΔQ = 0 C. P V

23. For the following P vs. V diagram is an Isothermal Process
Isothermal Process: Temperature is constant
How does the 1st Law Equation change during an Isothermal process?
The isothermal process happens at a constant temperature. The pressure and volume change, so work is done, but ΔU is zero. D. P V
PV = nRT = constant!
Take our graphing calc, graph y = 1/x, y = 2/x y = 3/x (isotherms!)
Why is the graph shaped the way it is? P = constant/V or V = constant/P

24. Summary of Processes

25. PV Diagrams
Used when the pressure and volume are known at each step of the process
The work done on a gas that takes it from some initial state to some final state is the negative of the area under the curve on the PV diagram
W = -PV
This is true whether or not the pressure stays constant

26. PV Diagrams, cont.
The curve on the diagram is called the path taken between the initial and final states
The work done depends on the particular path
Same initial and final states, but different amounts of work are done

27. 1st Law incomplete
Conservation of Energy, however processes that do conserve energy, still don’t appear to happen! WHY!?
A coffee cup breaks spontaneously but is unable to get put back together spontaneously
Clausius statement: “it is impossible for a self acting machine working in a cyclic process without any external force, to transfer heat from a body at a lower temperature to a body at a higher temperature.”

28. Second Law of Thermodynamics
Constrains the First Law
Establishes which processes actually occur
Heat engines are an important application

29. Heat Engine
A heat engine takes in energy by heat and partially converts it to other forms
In general, a heat engine carries some working substance through a cyclic process

30. Heat Engine, cont.
Energy is transferred from a source at a high temperature (Qh)
Work is done by the engine (Weng)
Energy is expelled to a source at a lower temperature (Qc)

31. Heat Engine, cont. Since it is a cyclical process, ∆U = 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

32. Heat Pumps and Refrigerators
Heat engines can run in reverse
Energy is injected
Energy is extracted from the cold reservoir
Energy is transferred to the hot reservoir
This process means the heat engine is running as a heat pump
A refrigerator is a common type of heat pump
An air conditioner is another example of a heat pump

33. PV-Diagrams
Pressure/Volume graphs are of tremendous value in analyzing the performance of heat engines. Essentially, the amount of work produced by an engine depends on the path it takes (changes in pressure and volume)

34. PV-Diagrams Let’s start slow
Engines follow a path, in this case from 1 2, 23, 34, and 41
Each affects the Work done by, or done on the System

35. Net Work of a Machine
Let’s study the engine to the right… Q: is the direction of the arrows important?

36. Net Work of a Machine
Let’s study the engine to the right… Q: is the direction of the arrows important? YES! Challenge is if work is done ON the system or BY the system Note: Please write down the work done for each of the next four steps

37. Step 1: Process a  b represents an isobaric compression of a gas
From a to b, the pressure remains constant – its value is P1. The volume decrease from V1 to V2. This represents work done on the system. How can you calculate the W?

38. Step 1: Process a  b represents an isobaric compression of a gas
From a to b, the pressure remains constant – its value is P1. The volume decrease from V1 to V2. This represents work done on the system. How can you calculate the W?

39. Step 2: Process b  c is an isochoric compression
Isochoric because the volume does not change but the pressure increases. What is the work for this step? ZERO!!!

40. Step 3: Process c  d is an isobaric expansion.
The gas expands from V1 to V2, doing work as it expands. The amount of work is equal to the area under the curve.

41. Step 4: Process d  a is an isochoric expansion
Volume stays constant. So no work is done. Pressure decreases.

42. Complete Cycle
Based on what you have recorded for the work on each step, what is the total work done on the system?

43. Complete Cycle
Based on what you have recorded for the work on each step, what is the total work done on the system? OR just the area of the enclosed area!

44. Overall

45. Question 1:
A substance undergoes a cyclic process shown in the graph. Heat transfer occurs during each process in the cycle.
What is the work output during process a  b?
How much work input is required during process b  c?
What is the net work done during the cycle
Note: 1 atm = x 105 Pa
Note: 1 L = m3

46. Question 1:
A substance undergoes a cyclic process shown in the graph. Heat transfer occurs during each process in the cycle.
-1.22 x 104 J (Expansion process, so work is done on surroundings)
4.05 x 103 J
-8.15 x 103 J

47. Question 1:

48. Question 2:
A heat engine’s cycle is shown in the PV diagram to the right.
P1 = 345 kPa, P2 = 245 kPa, P3 = 125 k Pa, and P4 = 225 kPa. V1 = 35.0 L and V2 = 85.0 L.
What is the net work done during one cycle of the engine?
Note: 1 L = m3

49. Question 2:
A heat engine’s cycle is shown in the PV diagram to the right.
P1 = 345 kPa, P2 = 245 kPa, P3 = 125 k Pa, and P4 = 225 kPa. V1 = 35.0 L and V2 = 85.0 L.
What is the net work done during one cycle of the engine?
Note: 1 L = m3
Ans: kJ

50. Question 2:

51. Second Law of Thermodynamics
No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely for the performance of an equal amount of work
Kelvin – Planck statement
Means that Qc cannot equal 0
Some Qc must be expelled to the environment
Means that e must be less than 100%

52. Thermal Efficiency of a Heat Engine
Thermal efficiency is defined as the ratio of the work done by the engine to the energy absorbed at the higher temperature
e = 1 (100% efficiency) only if Qc = 0
No energy expelled to cold reservoir

53. Derivation

54. Heat Pump The work is what you pay for The Qc is the desired benefit
The coefficient of performance (COP) measures the performance of the heat pump running in cooling mode

55. Heat Pump, COP In cooling mode, The higher the number, the better
A good refrigerator or air conditioner typically has a COP of 5 or 6

56. Heat Pump, COP In heating mode,
The heat pump warms the inside of the house by extracting heat from the colder outside air
Typical values are greater than one

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

58. 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
Carnot’s Theorem: No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs

59. Carnot Cycle

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

61. 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

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

63. 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 WCD

64. Carnot Cycle, PV Diagram
The work done by the engine is shown by the area enclosed by the curve
The net work is equal to Qh - Qc

65. 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

66. 2nd Law of Thermodynamics
Efficiency ≠ 100%
The Carnot Cycle represents the MAXIMUM efficiency for a heat engine
Isothermal exp.
Adiabatic exp.
Isothermal comp.
Adiabatic comp.

67. Notes About Carnot Efficiency
Efficiency is 0 if Th = Tc
Efficiency is 100% only if Tc = 0 K
Such reservoirs are not available
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

68. Real Engines Compared to Carnot Engines
All real engines are less efficient than the Carnot engine
Real engines are irreversible because of friction
Real engines are irreversible because they complete cycles in short amounts of time

69. Efficiency of Carnot Cycle

70. Second Law of Thermodynamics
Second: The entropy of a closed system never decreases as time goes by. Reversible processes do not change the entropy of a system, while irreversible processes increase a system’s entropy. S ≥ 0 S = Entropy of a System

71. Entropy
A state variable related to the Second Law of Thermodynamics, the entropy
Let Qr be the energy absorbed or expelled during a reversible, constant temperature process between two equilibrium states. Then the change in entropy during any constant temperature process connecting the two equilibrium states can be defined as the ratio of the energy to the temperature

72. Entropy, cont. Mathematically,
This applies only to the reversible path, even if the system actually follows an irreversible path
To calculate the entropy for an irreversible process, model it as a reversible process
When energy is absorbed, Q is positive and entropy increases
When energy is expelled, Q is negative and entropy decreases

73. More About Entropy Note, the equation defines the change in entropy
The entropy of the Universe increases in all natural processes
This is another way of expressing the Second Law of Thermodynamics
There are processes in which the entropy of a system decreases
If the entropy of one system, A, decreases it will be accompanied by the increase of entropy of another system, B.
The change in entropy in system B will be greater than that of system A.

74. Perpetual Motion Machines
A perpetual motion machine would operate continuously without input of energy and without any net increase in entropy
Perpetual motion machines of the first type would violate the First Law, giving out more energy than was put into the machine
Perpetual motion machines of the second type would violate the Second Law, possibly by no exhaust
Perpetual motion machines will never be invented

75. Entropy and Disorder Entropy can be described in terms of disorder
A disorderly arrangement is much more probable than an orderly one if the laws of nature are allowed to act without interference
This comes from a statistical mechanics development

76. Entropy and Disorder, cont.
Isolated systems tend toward greater disorder, and entropy is a measure of that disorder
S = kB ln W
kB is Boltzmann’s constant
W is a number proportional to the probability that the system has a particular configuration
This gives the Second Law as a statement of what is most probable rather than what must be
The Second Law also defines the direction of time of all events as the direction in which the entropy of the universe increases

77. Heat Death of the Universe
The entropy of the Universe always increases
The entropy of the Universe should ultimately reach a maximum
At this time, the Universe will be at a state of uniform temperature and density
This state of perfect disorder implies no energy will be available for doing work
This state is called the heat death of the Universe