Phase%20Changes%20and%20Latent%20Heat

1
Phase Changesand Latent Heat
Gas
Solid
Liquid

• Wheres the heat?

2
Reading

• Hess
• Phase Diagram
• pp 49 51
• Dew Point, Wet Bulb Temperature and Wet Bulb
  Potential Temperature
• pp 60 63
• Bohren Albrecht
• pp 218-223
• Wallace Hobbs
• p. 84

3
Objectives

• Be able to describe the changes in temperature,
  equilibrium pressure, volume and heat during
  various phase changes

4
Objectives

• Be able to recall from memory the definition of
  critical point
• Be able to recall from memory the definition of
  triple point

5
Objectives

• Be able recall from memory the values of
  temperature and pressure for the triple point of
  water
• Be able to recall from memory the values of
  temperature and pressure at the critical point of
  water

6
Objectives

• Be able to show isobaric, isochoric and
  isothermal changes on phase diagrams
• Be able to determine changes of boiling and
  melting temperatures with changes in atmospheric
  pressure

7
Objectives

• Be able to recall from memory the definition of
  latent heat
• Be able to determine whether latent heat is
  released or absorbed during a phase change
• Be able to provide the name given to each type of
  phase change

8
Objectives

• Be able to describe how enthalpy and latent heat
  are related
• Be able to perform calculations to determine the
  amount of latent heat released during a phase
  change
• Be able to perform calculations to determine the
  change in latent heat with temperature

9
Objective

• Be able to recall from memory the definition of
  wet bulb temperature
• Be able to compare the differences between wet
  bulb temperature and dew point temperature

10
Phase Changes

• Phase change results in a transformation of the
  molecular structure

Solid
Liquid
Gas
11
Phase Change

• Temperature of substance does not change during
  transformation

12
Phase Change

• Equilibrium (or saturation) pressure does not
  change during phase change

13
Phase Change

• Can Occur at Various Temperatures and Equilibrium
  Pressures

Water
Pressure (e)
T5
Ice
Vapor
Water Vapor
T4
T3
T2
Ice Vapor
T1
Volume (V)
14
Phase Change

• Volume changes significantly during phase change

Condensation
15
Phase Change

• Entropy also changes

Increasing Entropy
Solid
Liquid
Gas
16
Phase Change

• Phase Change (P-V Diagram)

• Vapor to Ice
• Water to Ice
• Triple Line
• The thermodynamic state at which three phases of
  a substance exist in equilibrium.

Ice Water
Water
Pressure (e)
Water Vapor
Vapor
Ice
Triple Line
0oC
Ice Vapor
T
Volume (V)
17
Phase Change

• Phase Change (P-V Diagram)

• Triple Line
• T 273.16K
• es 6.107 mb

Ice Water
Water
Pressure (e)
Water Vapor
Vapor
Ice
Triple Line
0oC
Ice Vapor
T
Volume (V)
18
Phase Change

• Phase Change (P-V Diagram)

• Vapor to Water
• Critical Point (Pc)
• The thermodynamic state in which liquid and gas
  phases of a substance coexist in equilibrium at
  the highest possible temperature.

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Phase Change

• Phase Change (P-V Diagram)

• Vapor to Water
• Critical Point (Pc)
• No liquid phase can exist at temperatures higher
  than the critical temperature
• Tc 647 K
• Pc 222,000 mb

20
Phase Change

• Phase Change (P-T Diagram)

esw
Liquid
Pressure
Solid
Gas
esi
Temperature
21
Phase Change

• Isothermal Compression

esw
Liquid
Pressure
Solid
Gas
esi
Temperature
22
Phase Change

• Isobaric Cooling

esw
Liquid
Pressure
Solid
Gas
esi
Temperature
23
Phase Change

• Changes in Atmospheric Pressure

• Change in Freezing Point

-.007oC atm-1
Liquid
Solid
Pressure
Gas
Temperature
24
Phase Change

• Changes in Atmospheric Pressure

• Change in Boiling Point

Liquid
Solid
Pressure
Gas
Temperature
25
Phase Change

• Critical Point

Critical Point
Liquid
Pressure
Solid
Gas
esi
Temperature
26
Phase Change

• Triple Point

Critical Point
Liquid
Pressure
Solid
Triple Point
6.11 mb
Gas
esi
0.01oC
Temperature
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Three Dimensional Phase Diagram
28
Three Dimensional Phase Diagram
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Phase Change

• Liquid Water Molecule
• Hydrogen Bonds
• Shearing Energy too great

30
Phase Change

• Ice
• Volume Increases

31
Phase Change

• Heat is absorbed or released during the phase
  changes

32
Phase Change

• Heat Absorbed

Sublimation
Gas
Evaporation
Solid
Liquid
Melting
33
Phase Change

• Heat Released

Deposition
Gas
Condensation
Solid
Liquid
Freezing
34
Phase Change

• Latent Heat
• The heat required to change the molecular
  configuration of a substance

Solid
Liquid
Gas
35
Phase Change

• Latent Heat

Sublimation (ls)
Gas
Vaporization (lv)
Solid
Liquid
Fusion (lf)
36
Phase Change

• Latent Heat
• Increase in internal energy results from the
  change in molecular configuration

Solid
Liquid
Gas
37
Latent Heat

• First Law of Thermodynamics
• Internal Energy changes
• Temperature is constant!
• Pressure is constant
• Volume changes
• Work is done

38
Latent Heat

• Rearrange

• For a phase change from liquid to vapor

av specific volume of vapor aw specific
volume of liquid
39
Latent Heat

• Substitute
• Into

• Define the change in Internal Energy

uv internal energy of vapor uw internal
energy of liquid
40
Latent Heat

• Latent Heat (lv) Change in Heat (dq)

• Rearrange

41
Latent Heat

• Enthalpy is defined as

• Substitute

or

• Latent Heat is a change in Enthalpy!

42
Latent Heat

• Latent Heat of Transformation (l)
• ratio of the heat absorbed (Q) to the mass
  undergoing a phase change

43
Latent Heat

• The amount of heat absorbed (or released) during
  a phase change is

44
Latent Heat

• Representative Values at 0oC
• Latent Heat of Fusion (lf)
• 3.34x105 J kg-1
• Latent Heat of Vaporization (lv)
• 2.500x106 J kg-1

45
Latent Heat

• Latent Heat of Sublimation (ls) at 0oC
• ls lf lv
• ls 2.834x106 J kg-1

46
Latent Heat

• Varies with temperature

Water
dQ
Pressure (e)
dQ
Ice
Vapor
dQ
0oC
dQ
T
Volume (V)
47
Variation of Latent Heat

• Lets examine the latent heat of vaporization

• Its easier to show the variation using entropy,
  but well follow Hess

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Variation of Latent Heat

• First Law of Thermodynamics

• Substitute

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Variation of Latent Heat

• Expand

• And since aw ltlt av

50
Variation of Latent Heat

• The Ideal Gas Law (or Equation of State)

• Substitute

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Variation of Latent Heat

• Differentiate with respect to temperature

52
Variation of Latent Heat

• Remember from your early childhood

cvv specific heat of vapor at a constant volume
53
Variation of Latent Heat

• The internal energy of water is a little more
  tricky!

54
Variation of Latent Heat

• Back to the First Law

• Differentiate with respect to temperature for
  water (remembering es is constant)

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Variation of Latent Heat

• But the change in specific volume of water with
  temperature is very small

cw specific heat of liquid water
56
Variation of Latent Heat

• Substitute into

57
Variation of Latent Heat

• Another repressed memory ...

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Variation of Latent Heat

• Change in the Latent Heat of Vaporization with
  Temperature
• Difference between
• Specific Heat of Vapor (at constant pressure)
• Specific Heat of Liquid Water

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Latent Heat

• Evaluate

cpv specific heat of vapor 1952 J K-1 kg-1 cw
specific heat of liquid water 4218 J K-1 kg-1
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Latent Heat

• Is this a factor to be considered?

lv latent heat of vaporization _at_ 273.16K 2.5
x 106 J kg-1
61
Latent Heat

• A small factor

62
Summary

• Specific Heat
• The amount of heat required to raise the
  temperature of a unit mass of a substance by one
  degree

63
Summary

• Specific Heat
• Dry Air
• Constant Volume
• cv 717 J K-1 kg-1
• Constant Pressure
• cp 1004 J K-1 kg-1

64
Summary

• Specific Heat
• Water Vapor
• Constant Volume
• cvv 1463 J K-1 kg-1
• Constant Pressure
• cpv 1870 J K-1 kg-1

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Summary

• Specific Heat
• Liquid Water (0oC)
• cw 4218 J K-1 kg-1
• cw 1 cal g-1 K-1
• Ice (0oC)
• ci 2106 J K-1 kg-1

66
Summary

• First Law of Thermodynamics

• For an isobaric process

67
Summary

• Latent Heat
• The heat required to change the molecular
  configuration of a substance

Solid
Liquid
Gas
68
Summary

• Latent Heat
• The change in enthalpy between states

69
Summary

• Latent Heat
• The amount of heat absorbed (or released) during
  a phase change

Sublimation (ls)
Gas
Vaporization (lv)
Solid
Liquid
Fusion (lf)
70
Summary

• Latent Heat
• The ratio of the heat absorbed (Q) to the mass
  undergoing a phase change

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Summary

• Latent Heat
• Vaporization
• lv 2.50 x 106 J kg-1
• Fusion
• lf 3.34 x 105 J kg-1
• Sublimation
• ls 2.834 x 106 J kg-1

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Moisture Variables

• Wet-Bulb Temperature (Tw)
• The temperature to which air is cooled by
  evaporating water into it at constant pressure
  until the air is saturated

Tw
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Moisture Variables

• Wet Bulb Temperature (Tw)
• Two methods to compute
• Thermodynamic (or Isobaric) Method
• Adiabatic Method

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Themodynamic Wet Bulb Temperature

• Different than Dew Point Temperature

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Moisture Variables

• Dew Point (Td)
• Temperature to which air must be cooled at
  constant pressure in order for it to become
  saturated with respect to liquid water

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Dew Point Temperature
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Thermodynamic Wet Bulb Temperature
es
Pressure
RH 100
Evaporation
De
Tatmosphere
Td
Tw
Temperature
78
Thermodynamic Wet Bulb Temperature

• Moisture is added to the atmosphere by
  evaporation
• Heat for evaporation comes from air and water

79
Thermodynamic Wet Bulb Temperature

• Heat Balance

Tw
Heat required to vaporize water
Heat lost by air

dQ
cp specific heat of air cw specific heat of
water mv mass of water that evaporates lv
latent heat of vaporization
dQ
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Thermodynamic Wet Bulb Temperature
Tw
cpd specific heat of dry air cpv
specific heat of water vapor cw specific
heat of liquid water md mass of dry air mv
mass of water vapor
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Thermodynamic Wet Bulb Temperature
Tw
Tw
w
Tw wet bulb temperature Ta temperature of the
air
T
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Thermodynamic Wet Bulb Temperature
Tw
Tw
mvsat mass of water vapor of saturated
air mvunsat mass of water vapor of unsaturated
air mvunsat- mvunsat amount of water vapor
evaporated into air
w
T
83
Thermodynamic Wet Bulb Temperature
Tw

• Divide both sides by md

Tw
w
T
wsat mixing ratio of saturated air wunsat
mixing ratio of unsaturated air
84
Thermodynamic Wet Bulb Temperature
Tw

• As md increases, wcpv and mw/md decreases
• Can be neglected

Tw
w
T
85
Thermodynamic Wet Bulb Temperature
Tw

• Substitute for mixing ratio

Tw
w
T
86
Thermodynamic Wet Bulb Temperature
Tw

• Solve for e

Tw
w
T
87
Thermodynamic Wet Bulb Temperature

• Psychrometric Equation

Tw

• Psychrometric Constant

Tw
w
T
88
Thermodynamic Wet Bulb Temperature

• Other Factors
• Ventilation
• Radiation
• Instrumentation

Tw
w
Tw
w
T
89
Thermodynamic Wet Bulb Temperature
Tw

• Measure T Tw
• esat is a Function of Tw via Claussius-Clapeyron
• e is a Function of T via Claussius-Clapeyron

w
Tw
w
T,ws
90
Thermodynamic Wet Bulb Temperature

• Must Be Solved Iteratively or..

91
Thermodynamic Wet Bulb Temperature

• Psychrometric Charts
• Equation Solved for Various Temperatures

92
Thermodynamic Wet Bulb Temperature

• Psychrometric Tables

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Adiabatic Wet Bulb Temperature

• The temperature an air parcel would have if
  cooled to saturation and then compressed
  adiabatically to the original pressure in a moist
  adiabatic process

94
Adiabatic Wet Bulb Temperature
T
Td
Tw
95
Wet Bulb Potential Temperature (qw )

• The wet bulb temperature the air would have if it
  were expanded or compressed adiabatically from
  its existing pressure and wet bulb temperature to
  a standard pressure of 1000 mb.

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