1. Energy in Thermal Processes: First Law of Thermodynamics
Chapter 17
Energy in Thermal Processes:
First Law of Thermodynamics

2. Thermodynamics – Historical Background
Thermodynamics and mechanics were considered to be separate branches
Until about 1850
Experiments by James Joule and others showed a connection between them
A connection was found between the transfer of energy by heat in thermal processes and the transfer of energy by work in mechanical processes
The concept of energy was generalized to include internal energy
The Law of Conservation of Energy emerged as a universal law of nature

3. James Prescott Joule 1818 – 1889 Largely self-educated
Work led to establishing Conservation of Energy
Determined the mechanical equivalent of heat

4. Internal Energy
Internal energy is all the energy of a system that is associated with its microscopic components
These components are its atoms and molecules
The system is viewed from a reference frame at rest with respect to the system

5. Internal Energy and Other Energies
The kinetic energy due to its motion through space is not included
Internal energy does include kinetic energies due to
Random translational motion
Rotational motion
Vibrational motion
Internal energy also includes intermolecular potential energy

6. Heat
Heat is a mechanism by which energy is transferred between a system and its environment due to a temperature difference between them
The term heat will also be used to represent the amount of energy, Q, transferred by this mechanism

7. Heat vs. Work
Work done on or by a system is a measure of the amount of energy transferred between the system and its surroundings
Heat is energy that has been transferred between a system and its surroundings due to a temperature difference

8. Units of Heat Historically, the calorie was the unit used for heat
One calorie is the heat necessary to raise the temperature of 1 g of water from 14.5o C to 15.5o C
The Calorie used for food is actually 1 kcal
In the US Customary system, the unit is a BTU (British Thermal Unit)
One BTU is the heat required to raise the temperature of 1 lb of water from 63o F to 64o F
The standard in the text is to use Joules

9. Mechanical Equivalent of Heat
1 cal = J
This is known as the mechanical equivalent of heat
It is the current definition of a calorie
The Joule as the SI unit of heat was adopted in 1948

10. Specific Heat
Specific heat, c, is the heat amount of energy per unit mass required to change the temperature of a substance by 1°C
If energy Q transfers to a sample of a substance of mass m and the temperature changes by DT, then the specific heat is

11. Specific Heat, cont
The specific heat is essentially a measure of how insensitive a substance is to the addition of energy
The greater the substance’s specific heat, the more energy that must be added to cause a particular temperature change
The equation is often written in terms of Q: Q = m c DT
Units of specific heat are J/ k.°C

12. Some Specific Heat Values

13. More Specific Heat Values

14. Sign Conventions If the temperature increases:
Q and DT are positive
Energy transfers into the system
If the temperature decreases:
Q and DT are negative
Energy transfers out of the system

15. Specific Heat of Water
Water has the highest specific heat of most common materials
Hydrogen and helium have higher specific heats
This is responsible for many weather phenomena
Moderate temperatures near large bodies of water
Global wind systems
Land and sea breezes

16. Calorimetry
One technique for measuring specific heat involves heating a material, adding it to a sample of water, and recording the final temperature
This technique is known as calorimetry
A calorimeter is a device in which this energy transfer takes place

17. Calorimetry, cont The system of the sample and the water is isolated
The calorimeter allows no energy to enter or leave the system
Conservation of energy requires that the amount of energy that leaves the sample equals the amount of energy that enters the water
Conservation of Energy gives a mathematical expression of this: Qcold= - Qhot

18. Calorimetry, final
The negative sign in the equation is critical for consistency with the established sign convention
Since each Q = m c DT, cunknown can be found
Technically, the mass of the water’s container should be included, but if mw>>mcontainer it can be neglected

19. Phase Changes
A phase change is when a substance changes from one form to another
Two common phase changes are
Solid to liquid (melting)
Liquid to gas (boiling)
During a phase change, there is no change in temperature of the substance

20. Latent Heat
Different substances react differently to the energy added or removed during a phase change
Due to their different molecular arrangements
The amount of energy also depends on the mass of the sample
If an amount of energy Q is required to change the phase of a sample of mass m,

21. Latent Heat, cont
The quantity L is called the latent heat of the material
Latent means hidden
The value of L depends on the substance as well as the actual phase change

22. Latent Heat, final
The latent heat of fusion, Lf, is used during melting or freezing
The latent heat of vaporization, Lv, is used when the phase change boiling or condensing
The positive sign is used when the energy is transferred into the system
This will result in melting or boiling
The negative sign is used when energy is transferred out of the system
This will result in freezing or condensation

23. Sample Latent Heat Values

24. Graph of Ice to Steam

25. Warming Ice, Graph Part A
Start with one gram of ice at –30.0º C
During A, the temperature of the ice changes from –30.0º C to 0º C
Use Q = m cice ΔT
In this case, 62.7 J of energy are added

26. Melting Ice, Graph Part B
Once at 0º C, the phase change (melting) starts
The temperature stays the same although energy is still being added
Use Q = m Lf
The energy required is 333 J
On the graph, the values move from 62.7 J to 396 J

27. Warming Water, Graph Part C
Between 0º C and 100º C, the material is liquid and no phase changes take place
Energy added increases the temperature
Use Q = m cwater ΔT
419 J are added
The total is now 815 J

28. Boiling Water, Graph Part D
At 100º C, a phase change occurs (boiling)
Temperature does not change
Use Q = m Lv
This requires2260 J
The total is now 3070 J

29. Heating Steam
After all the water is converted to steam, the steam will heat up
No phase change occurs
The added energy goes to increasing the temperature
Use Q = m csteam ΔT
In this case, 40.2 J are needed
The temperature is going to 120o C
The total is now 3110 J

30. State Variables State variables describe the state of a system
In the macroscopic approach to thermodynamics, variables are used to describe the state of the system
Pressure, temperature, volume, internal energy
These are examples of state variables
The macroscopic state of an isolated system can be specified only if the system is in internal thermal equilibrium

31. Transfer Variables
Transfer variables have values only when a process occurs in which energy is transferred across the boundary of a system
Transfer variables are not associated with any given state of the system, only with changes in the state
Heat and work are transfer variables
Example of heat: we can only assign a value of the heat if energy crosses the boundary by heat

32. Work in Thermodynamics
Work can be done on a deformable system, such as a gas
Consider a cylinder with a moveable piston
A force is applied to slowly compress the gas
The compression is slow enough for all the system to remain essentially in thermal equilibrium
This is said to occur in a quasi-static process
A simplification model

33. Work, 2
The piston is pushed downward by a force through a displacement:
A.dy is the change in volume of the gas, dV
Therefore, the work done on the gas is dW = -P dV

34. Work, 3 Interpreting dW = - P dV The total work done is
If the gas is compressed, dV is negative and the work done on the gas is positive
If the gas expands, dV is positive and the work done on the gas is negative
If the volume remains constant, the work done is zero
The total work done is

35. PV Diagrams
Used when the pressure and volume are known at each step of the process
The state of the gas at each step can be plotted on a graph called a PV diagram
This allows us to visualize the process through which the gas is progressing
The curve is called the path

36. PV Diagrams, cont
The work done on a gas in a quasi-static process that takes the gas from an initial state to a final state is the negative of the area under the curve on the PV diagram, evaluated between the initial and final states
This is true whether or not the pressure stays constant
The work done does depend on the path taken

37. Work Done By Various Paths
Each of these processes have the same initial and final states
The work done differs in each process
The work done depends on the path

38. Work From A PV Diagram, Example 1
The volume of the gas is first reduced from Vi to Vf at constant pressure Pi
Next, the pressure increases from Pi to Pf by heating at constant volume Vf
W = -Pi(Vf – Vi)

39. Work From A PV Diagram, Example 2
The pressure of the gas is increased from Pi to Pf at a constant volume
The volume is decreased from Vi to Vf
W = -Pf(Vf – Vi)

40. Work From A PV Diagram, Example 3
The pressure and the volume continually change
The work is some intermediate value between –Pf(Vf – Vi) and –Pi(Vf – Vi)
To evaluate the actual amount of work, the function P(V) must be known

41. Heat Transfer, Example 1
The energy transfer, Q, into or out of a system also depends on the process
The energy reservoir is a source of energy that is considered to be so great that a finite transfer of energy does not change its temperature
The piston is pushed upward, the gas is doing work on the piston

42. Heat Transfer, Example 2
This gas has the same initial volume, temperature and pressure as the previous example
The final states are also identical
No energy is transferred by heat through the insulating wall
No work is done by the gas expanding into the vacuum

43. Energy Transfer, Summary
Energy transfers by heat, like the work done, depend on the initial, final, and intermediate states of the system
Both work and heat depend on the path taken
Both depend on the process followed between the initial and final states of the system

44. The First Law of Thermodynamics
The First Law of Thermodynamics is a special case of the Law of Conservation of Energy
It takes into account changes in internal energy and energy transfers by heat and work
The First Law of Thermodynamics states that DEint = Q + W
A special case of the continuity equation
All quantities must have the same units of measure of energy

45. The First Law of Thermodynamics, cont
For infinitesimal changes in a system dEint = dQ + dW
No practical distinction exists between the results of heat and work on a microscopic scale
Each can produce a change in the internal energy of the system
Once a process or path is defined, Q and W can be calculated or measured

46. Adiabatic Process
An adiabatic process is one during which no energy enters or leaves the system by heat
Q = 0
This is achieved by
Thermally insulating the walls of the system
Having the process proceed so quickly that no heat can be exchanged

47. Adiabatic Process, cont
Since Q = 0, DEint = W
If the gas is compressed adiabatically, W is positive so DEint is positive and the temperature of the gas increases
Work is done on the gas
If the gas is expands adiabatically the temperature of the gas decreases

48. Adiabatic Processes, Examples
Some important examples of adiabatic processes related to engineering are
The expansion of hot gases in an internal combustion engine
The liquefaction of gases in a cooling system
The compression stroke in a diesel engine

49. Adiabatic Free Expansion
This is an example of adiabatic free expansion
The process is adiabatic because it takes place in an insulated container
Because the gas expands into a vacuum, it does not apply a force on a piston and W = 0
Since Q = 0 and W = 0, DEint = 0 and the initial and final states are the same
No change in temperature is expected

50. Isobaric Process
An isobaric process is one that occurs at a constant pressure
The values of the heat and the work are generally both nonzero
The work done is W = P (Vf – Vi) where P is the constant pressure

51. Isovolumic Process
An isovolumic process is one in which there is no change in the volume
Since the volume does not change, W = 0
From the First Law, DEint = Q
If energy is added by heat to a system kept at constant volume, all of the transferred energy remains in the system as an increase in its internal energy

52. Isothermal Process
An isothermal process is one that occurs at a constant temperature
Since there is no change in temperature, DEint = 0
Therefore, Q = - W
Any energy that enters the system by heat must leave the system by work

53. Isothermal Process, cont
This is a PV diagram of an isothermal expansion
The curve is a hyperbola
The curve is called an isotherm

54. Isothermal Expansion, Details
The curve of the PV diagram indicates PV = constant
The equation of a hyperbola
The work done on the ideal gas can be calculated by

55. Special Processes, Summary
Adiabatic
No heat exchanged
Q = 0 and DEint = W
Isobaric
Constant pressure
W = P (Vf – Vi) and DEint = Q + W
Isothermal
Constant temperature
DEint = 0 and Q = - W

56. Cyclic Processes
A cyclic process is one that originates and ends at the same state
This process would not be isolated
On a PV diagram, a cyclic process appears as a closed curve
The internal energy must be zero since it is a state variable
If DEint = 0, Q = -W
In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PV diagram

57. Molar Specific Heat
Several processes can change the temperature of an ideal gas
Since DT is the same for each process, DEint is also the same
The heat is different for the different paths
The heat associated with a particular change in temperature is not unique

58. Molar Specific Heat, 2
We define specific heats for two processes that frequently occur
Changes with constant pressure
Changes with constant volume
Using the number of moles, n, we can define molar specific heats for these processes

59. Molar Specific Heat, 3 Molar specific heats:
Q = n Cv DT for constant volume processes
Q = n Cp DT for constant pressure processes
Q (in a constant pressure process) must account for both the increase in internal energy and the transfer of energy out of the system by work
Q(constant P) > Q(constant V) for given values of n and DT

60. Ideal Monatomic Gas A monatomic gas contains one atom per molecule
When energy is added to a monatomic gas in a container with a fixed volume, all of the energy goes into increasing the translational kinetic energy of gas
There is no other way to store energy in such a gas

61. Ideal Monatomic Gas, cont
Therefore, Eint = 3/2 n R T
E is a function of T only
In general, the internal energy of an ideal gas is a function of T only
The exact relationship depends on the type of gas
At constant volume, Q = DEint = n Cv DT
This applies to all ideal gases, not just monatomic ones

62. Monatomic Gases, final
Solving for Cv gives Cv = 3/2 R = 12.5 J/mol . K
For all monatomic gases
This is in good agreement with experimental results for monatomic gases
In a constant pressure process, DEint = Q + W and Cp – Cv = R
This also applies to any ideal gas
Co = 5/2 R = 20.8 J/mol. K

63. Ratio of Molar Specific Heats
We can also define
Theoretical values of CV, CP, and g are in excellent agreement for monatomic gases

64. Sample Values of Molar Specific Heats

65. Adiabatic Process for an Ideal Gas
At any time during the process, PV = nRT is valid
None of the variables alone are constant
Combinations of the variables may be constant
The pressure and volume of an ideal gas at any time during an adiabatic process are related by PVg = constant
All three variables in the ideal gas law (P, V, T) can change during an adiabatic process

66. Equipartition of Energy
With complex molecules, other contributions to internal energy must be taken into account
One possible energy is the translational motion of the center of mass

67. Equipartition of Energy, 2
Rotational motion about the various axes also contributes
We can neglect the rotation around the y axis since it is negligible compared to the x and z axes

68. Equipartition of Energy, 3
The translational motion adds three degrees of freedom
The rotational motion adds two degrees of freedom
Therefore, Eint = 5/2 n R T and CV = 5/2 R = 20.8 J/mol.K
The model predicts that g = 7/5 = 1.40

69. Equipartition of Energy, 4
The molecule can also vibrate
There is kinetic energy and potential energy associated with the vibrations
This adds two more degrees of freedom

70. Equipartition of Energy, 5
Considering all the degrees of freedom:
Eint = 7/2 n R T
Cv = 7/2 R = 29.1 J / mol.K
g = 1.29
This doesn’t agree well with experimental results
A wide range of temperature needs to be included

71. Agreement with Experiment
Molar specific heat is a function of temperature
At low temperatures, a diatomic gas acts like a monatomic gas
CV = 3/2 R

72. Agreement with Experiment, cont
At about room temperature, the value increases to CV = 5/2 R
This is consistent with adding rotational energy but not vibrational energy
At high temperatures, the value increases to CV = 7/2 R
This includes vibrational energy as well as rotational and translational

73. Complex Molecules
For molecules with more than two atoms, the vibrations are more complex
The number of degrees of freedom is larger
The more degrees of freedom available to a molecule, the more “ways” there are to store energy
This results in a higher molar specific heat

74. Quantization of Energy
To explain the results of the various molar specific heats, we must use some quantum mechanics
Classical mechanics is not sufficient
The rotational and vibrational energies of a molecule are quantized

75. Quantization of Energy, 2
The energy level diagram shows the rotational and vibrational states of a diatomic molecule

76. Quantization of Energy, 3
The vibrational states are separated by larger energy gaps than are rotational states
At low temperatures, the energy gained during collisions is generally not enough to raise it to the first excited state of either rotation or vibration

77. Quantization of Energy, 4
Even though rotation and vibration are classically allowed, they do not occur
As the temperature increases, the energy of the molecules increases
In some collisions, the molecules have enough energy to excite to the first excited state
As the temperature continues to increase, more molecules are in excited states

78. Quantization of Energy, final
At about room temperature, rotational energy is contributing fully
At about 1000 K, vibrational energy levels are reached
At about K, vibration is contributing fully to the internal energy

79. Mechanisms of Heat Transfer
We want to know the rate at which energy is transferred
There are various mechanisms responsible for the transfer
Mechanisms include
Conduction
Convection
Radiation

80. Conduction The transfer can be viewed on an atomic scale
It is an exchange of kinetic energy between microscopic particles by collisions
The microscopic particles can be atoms, molecules or free electrons
Less energetic particles gain energy during collisions with more energetic particles
Rate of conduction depends upon the characteristics of the substance

81. Conduction, cont. In general, metals are good conductors
They contain large numbers of electrons that are relatively free to move through the metal
They can transport energy from one region to another
Poor conductors include asbestos, paper, gases
Conduction can occur only if there is a difference in temperature between two parts of the conducting medium

82. Conduction, equation
The slab allows energy to transfer from the region of higher temperature to the region of lower temperature
The rate of transfer is given by

83. Conduction, equation explanation
A is the cross-sectional area
Δx is the thickness of the slab
Or the length of a rod
Power is in Watts when Q is in Joules and t is in seconds
k is the thermal conductivity of the material
Good conductors have high k values and good insulators have low k values

84. Temperature Gradient
The quantity |dT / dx| is called the temperature gradient of the material
It measures the rate at which temperature varies with position
For a rod, the temperature gradient can be expressed as

85. Rate of Energy Transfer in a Rod
Using the temperature gradient for the rod, the rate of energy transfer becomes

86. Some Thermal Conductivities

87. Some More Thermal Conductivities

88. More Thermal Conductivities

89. Convection Energy transferred by the movement of a fluid
When the movement results from differences in density, it is called natural convection
When the movement is forced by a fan or a pump, it is called forced convection

90. Convection example
Air directly above the radiator is warmed and expands
The density of the air decreases, and it rises
A continuous air current is established

91. Radiation Radiation does not require physical contact
All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules
Rate of radiation is given by Stefan’s Law

92. Stefan’s Law P = σ A e T4 P is the rate of energy transfer, in Watts
σ = x 10-8 W/m2 K4
Stefan-Boltzmann constant
A is the surface area of the object
e is a constant called the emissivity
e varies from 0 to 1
The emissivity is also equal to the absorptivity
T is the temperature in Kelvins

93. Energy Absorption and Emission by Radiation
With its surroundings, the rate at which the object at temperature T with surroundings at To radiates is
Pnet = σ A e (T4 –To4)
When an object is in equilibrium with its surroundings, it radiates and absorbs at the same rate
Its temperature will not change

94. Earth’s Energy Balance
Energy arrives at the Earth by electro-magnetic radiation from the Sun
This energy is absorbed at the surface of the Earth and reradiated out into space
This follows Stefan’s Law
Assume any change in the temperature of the Earth over a time interval is (approximately) zero

95. Earth’s Energy Balance, 2
Energy from the Sun arrives from one direction
Energy is emitted by the Earth in all directions
From energy balance analysis, the temperature of the Earth should be about 255 K
The actual temperature is about 288 K, due to atmospheric affects