Phase Changes and Latent Heat Gas Solid Liquid
- Slides: 95
Phase Changes and Latent Heat Gas Solid Liquid Where’s the heat? Prof. Fred Remer University of North Dakota
Reading l Hess – Phase Diagram l pp 49 – 51 – Dew Point, Wet Bulb Temperature and Wet Bulb Potential Temperature l l pp 60 – 63 Bohren & Albrecht – pp 218 -223 l Wallace & Hobbs – p. 84 Prof. Fred Remer University of North Dakota
Objectives l Be able to describe the changes in temperature, equilibrium pressure, volume and heat during various phase changes Prof. Fred Remer University of North Dakota
Objectives Be able to recall from memory the definition of critical point l Be able to recall from memory the definition of triple point l Prof. Fred Remer University of North Dakota
Objectives Be able recall from memory the values of temperature and pressure for the triple point of water l Be able to recall from memory the values of temperature and pressure at the critical point of water l Prof. Fred Remer University of North Dakota
Objectives Be able to show isobaric, isochoric and isothermal changes on phase diagrams l Be able to determine changes of boiling and melting temperatures with changes in atmospheric pressure l Prof. Fred Remer University of North Dakota
Objectives Be able to recall from memory the definition of latent heat l Be able to determine whether latent heat is released or absorbed during a phase change l Be able to provide the name given to each type of phase change l Prof. Fred Remer University of North Dakota
Objectives Be able to describe how enthalpy and latent heat are related l Be able to perform calculations to determine the amount of latent heat released during a phase change l Be able to perform calculations to determine the change in latent heat with temperature l Prof. Fred Remer University of North Dakota
Objective Be able to recall from memory the definition of wet bulb temperature l Be able to compare the differences between wet bulb temperature and dew point temperature l Prof. Fred Remer University of North Dakota
Phase Changes l Phase change results in a transformation of the molecular structure Gas Prof. Fred Remer University of North Dakota Liquid Solid
Phase Change l Temperature of substance does not change during transformation T Prof. Fred Remer University of North Dakota
Phase Change l Equilibrium (or saturation) pressure does not change during phase change Prof. Fred Remer University of North Dakota
Phase Change Can Occur at Various Temperatures and Equilibrium Pressures Pressure (e) l Water Ice Water & Vapor Ice & Vapor Volume (V) Prof. Fred Remer University of North Dakota T 5 T 4 T 3 T 2 T 1
Phase Change l Volume changes significantly during phase change Condensation Prof. Fred Remer University of North Dakota
Phase Change l Entropy also changes Increasing Entropy Solid Prof. Fred Remer University of North Dakota Liquid Gas
Phase Change (P-V Diagram) – Vapor to Ice – Water to Ice – Triple Line l The thermodynamic state at which three phases of a substance exist in equilibrium. Ice & Water Pressure (e) l Water Ice Water & Vapor Triple Line Ice & Vapor Volume (V) Prof. Fred Remer University of North Dakota 0 o C T
Phase Change l Phase Change (P-V Diagram) – Triple Line T = 273. 16 K l es = 6. 107 mb l Pressure (e) Ice & Water Ice Water & Vapor Triple Line Ice & Vapor Volume (V) Prof. Fred Remer University of North Dakota 0 o C T
Phase Change l 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. Ice & Water Pressure (e) l Critical Point Water Ice Water & Vapor Ice & Vapor Volume (V) Prof. Fred Remer University of North Dakota 0 o C T
Phase Change l 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 Ice & Water Pressure (e) l Critical Point Water Ice Water & Vapor Ice & Vapor Volume (V) Prof. Fred Remer University of North Dakota 0 o C T
Phase Change (P-T Diagram) Pressure l Liquid es w Solid es i Gas Temperature Prof. Fred Remer University of North Dakota
Phase Change Isothermal Compression Pressure l Liquid es w Solid es i Gas Temperature Prof. Fred Remer University of North Dakota
Phase Change Isobaric Cooling Pressure l Solid Liquid es w Gas es i Temperature Prof. Fred Remer University of North Dakota
Phase Change l Changes in Atmospheric Pressure – Change in Freezing Point Pressure -. 007 o-1 C atm Liquid Solid Gas Temperature Prof. Fred Remer University of North Dakota
Phase Change l Changes in Atmospheric Pressure – Change in Boiling Point Liquid Solid Gas Temperature Prof. Fred Remer University of North Dakota
Phase Change Critical Point Pressure l Critical Point Liquid Solid es i Gas Temperature Prof. Fred Remer University of North Dakota
Phase Change Triple Point Pressure l Critical Point Liquid Solid Triple Point 6. 11 mb es i Gas 0. 01 o. C Temperature Prof. Fred Remer University of North Dakota
Three Dimensional Phase Diagram Prof. Fred Remer University of North Dakota Critical Point r e t Wa Ice Vapor Pressure Ice & Water (hidden) Water & Va Triple por S Ice & wtate ater Specifi c Volu me Va po r e r u at r e p m e T
Three Dimensional Phase Diagram Prof. Fred Remer University of North Dakota
Phase Change l Liquid Water Molecule – Hydrogen Bonds – Shearing Energy too great Prof. Fred Remer University of North Dakota
Phase Change l Ice – Volume Increases Prof. Fred Remer University of North Dakota
Phase Change l Heat is absorbed or released during the phase changes Gas Liquid Prof. Fred Remer University of North Dakota Solid
Phase Change l Heat Absorbed Evaporation Gas Solid Liquid Melting Prof. Fred Remer University of North Dakota Sublimation
Phase Change l Heat Released Condensation Gas Solid Liquid Freezing Prof. Fred Remer University of North Dakota Deposition
Phase Change l Latent Heat – The heat required to change the molecular configuration of a substance Gas Prof. Fred Remer University of North Dakota Liquid Solid
Phase Change l Latent Heat Vaporization (l v ) Gas Solid Liquid Fusion (lf) Prof. Fred Remer University of North Dakota Sublimation (l s )
Phase Change l Latent Heat – Increase in internal energy results from the change in molecular configuration Gas Prof. Fred Remer University of North Dakota Liquid Solid
Latent Heat l First Law of Thermodynamics – Internal Energy changes – Temperature is constant! – Pressure is constant – Volume changes l Prof. Fred Remer University of North Dakota Work is done
Latent Heat l Rearrange l For a phase change from liquid to vapor Prof. Fred Remer University of North Dakota av = specific volume of vapor aw = specific volume of liquid
Latent Heat l Substitute l Into l Define the change in Internal Energy uv = internal energy of vapor uw = internal energy of liquid Prof. Fred Remer University of North Dakota
Latent Heat l Latent Heat (lv) = Change in Heat (dq) l Rearrange Prof. Fred Remer University of North Dakota
Latent Heat l Enthalpy is defined as l Substitute or l Latent Heat is a change in Enthalpy! Prof. Fred Remer University of North Dakota
Latent Heat l Latent Heat of Transformation (l) – ratio of the heat absorbed (Q) to the mass undergoing a phase change Prof. Fred Remer University of North Dakota
Latent Heat l The amount of heat absorbed (or released) during a phase change is Prof. Fred Remer University of North Dakota
Latent Heat l Representative Values at 0 o. C – Latent Heat of Fusion (lf) l 3. 34 x 105 J kg-1 – Latent Heat of Vaporization (lv) l Prof. Fred Remer University of North Dakota 2. 500 x 106 J kg-1
Latent Heat of Sublimation (ls) at 0 o. C ls = l f + lv ls = 2. 834 x 106 J kg-1 Pressure l Liquid es w Solid Triple Point 6. 11 mb es i Gas 0. 01 o. C Temperature Prof. Fred Remer University of North Dakota
Latent Heat Varies with temperature Pressure (e) l Water Ice d. Q Vapor d. Q Volume (V) Prof. Fred Remer University of North Dakota 0 o. C T
Variation of Latent Heat l Let’s examine the latent heat of vaporization l It’s easier to show the variation using entropy, but we’ll follow Hess Prof. Fred Remer University of North Dakota
Variation of Latent Heat l First Law of Thermodynamics l Substitute Prof. Fred Remer University of North Dakota
Variation of Latent Heat l Expand l And since aw << av Prof. Fred Remer University of North Dakota
Variation of Latent Heat l The Ideal Gas Law (or Equation of State) l Substitute Prof. Fred Remer University of North Dakota
Variation of Latent Heat l Differentiate with respect to temperature Prof. Fred Remer University of North Dakota
Variation of Latent Heat l Remember from your early childhood cvv = specific heat of vapor at a constant volume Prof. Fred Remer University of North Dakota
Variation of Latent Heat l The internal energy of water is a little more tricky! Prof. Fred Remer University of North Dakota
Variation of Latent Heat l Back to the First Law l Differentiate with respect to temperature for water (remembering es is constant) Prof. Fred Remer University of North Dakota
Variation of Latent Heat l But the change in specific volume of water with temperature is very small Prof. Fred Remer University of North Dakota cw = specific heat of liquid water
Variation of Latent Heat l Substitute Prof. Fred Remer University of North Dakota into
Variation of Latent Heat l Another repressed memory. . . Prof. Fred Remer University of North Dakota
Variation of Latent Heat l Change in the Latent Heat of Vaporization with Temperature – Difference between Specific Heat of Vapor (at constant pressure) l Specific Heat of Liquid Water l Prof. Fred Remer University of North Dakota
Latent Heat l Evaluate cpv = specific heat of vapor = 1952 J K-1 kg-1 cw = specific heat of liquid water = 4218 J K-1 kg-1 Prof. Fred Remer University of North Dakota
Latent Heat l Is this a factor to be considered? lv = latent heat of vaporization @ 273. 16 K = 2. 5 x 106 J kg-1 Prof. Fred Remer University of North Dakota
Latent Heat l A small factor Prof. Fred Remer University of North Dakota
Summary l Specific Heat – The amount of heat required to raise the temperature of a unit mass of a substance by one degree Prof. Fred Remer University of North Dakota
Summary l Specific Heat – Dry Air l Constant Volume cv = 717 J K-1 kg-1 l Constant Pressure cp = 1004 J K-1 kg-1 Prof. Fred Remer University of North Dakota
Summary l Specific Heat – Water Vapor l Constant Volume – cvv = 1463 J K-1 kg-1 l Constant Pressure – cpv = 1870 J K-1 kg-1 Prof. Fred Remer University of North Dakota
Summary l Specific Heat – Liquid Water (0 o. C) cw = 4218 J K-1 kg-1 l cw = 1 cal g-1 K-1 l – Ice (0 o. C) l Prof. Fred Remer University of North Dakota ci = 2106 J K-1 kg-1
Summary l Latent Heat – The heat required to change the molecular configuration of a substance Gas Prof. Fred Remer University of North Dakota Liquid Solid
Summary l Latent Heat – The change in enthalpy between states Prof. Fred Remer University of North Dakota
Summary l Latent Heat – The amount of heat absorbed (or released) during a phase change Vaporization (l v ) Gas Solid Liquid Prof. Fred Remer University of North Dakota Sublimation (l s ) Fusion (lf)
Summary l Latent Heat – The ratio of the heat absorbed (Q) to the mass undergoing a phase change Prof. Fred Remer University of North Dakota
Summary l Latent Heat – Vaporization l lv = 2. 50 x 106 J kg-1 – Fusion l lf = 3. 34 x 105 J kg-1 – Sublimation l ls Prof. Fred Remer University of North Dakota = 2. 834 x 106 J kg-1
Moisture Variables l Wet-Bulb Temperature (Tw) – The temperature to which air is cooled by evaporating water into it at constant pressure until the air is saturated Prof. Fred Remer University of North Dakota Tw
Moisture Variables l Wet Bulb Temperature (Tw) – Two methods to compute Thermodynamic (or Isobaric) Method l Adiabatic Method l Prof. Fred Remer University of North Dakota
Themodynamic Wet Bulb Temperature l Different than Dew Point Temperature Tw Td Prof. Fred Remer University of North Dakota
Moisture Variables l 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 Prof. Fred Remer University of North Dakota Td
Pressure Dew Point Temperature es RH = 100% esaturation Isobaric Cooling Td Tatmosphere Temperature Prof. Fred Remer University of North Dakota
Pressure Thermodynamic Wet Bulb Temperature es RH = 100% De Evaporation Td Tw Tatmosphere Temperature Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature l Moisture is added to the atmosphere by evaporation l Heat for evaporation comes from air and water Prof. Fred Remer University of North Dakota Tw
Thermodynamic Wet Bulb Temperature l Heat Balance Tw Heat lost by air Heat required to = vaporize water d. Q cp = specific heat of air cw = specific heat of water mv = mass of water that evaporates lv = latent heat of vaporization Prof. Fred Remer University of North Dakota d. Q
Thermodynamic Wet Bulb Temperature Tw cp d cp v cw md mv = specific heat of dry air = specific heat of water vapor = specific heat of liquid water = mass of dry air = mass of water vapor Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature Tw Tw Tw = wet bulb temperature Ta = temperature of the air Prof. Fred Remer University of North Dakota w T
Thermodynamic Wet Bulb Temperature 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 Prof. Fred Remer University of North Dakota Tw w T
Thermodynamic Wet Bulb Temperature Tw l Divide both sides by md Tw w wsat = mixing ratio of saturated air wunsat = mixing ratio of unsaturated air Prof. Fred Remer University of North Dakota T
Thermodynamic Wet Bulb Temperature Tw l As md increases, wcpv and mw/md decreases – Can be neglected Tw w T Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature Tw l Substitute for mixing ratio Tw w T Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature Tw l Solve for e Tw w T Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature l Psychrometric Equation Tw l Psychrometric Constant Tw w T Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature l Other Factors – Ventilation – Radiation – Instrumentation Tw w’ T w w T Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature Tw Measure T & Tw l esat is a Function of Tw via Claussius-Clapeyron l e is a Function of T via Claussius-Clapeyron l Prof. Fred Remer University of North Dakota w’ T w w T, ws
Thermodynamic Wet Bulb Temperature l Must Be Solved Iteratively or…. . Prof. Fred Remer University of North Dakota
Thermodynamic Wet Bulb Temperature l Psychrometric Charts – Equation Solved for Various Temperatures Relative Humidity % Prof. Fred Remer University of North Dakota Dry Bulb o. F
Thermodynamic Wet Bulb Temperature l Psychrometric Tables Prof. Fred Remer University of North Dakota
Adiabatic Wet Bulb Temperature l The temperature an air parcel would have if cooled to saturation and then compressed adiabatically to the original pressure in a moist adiabatic process Prof. Fred Remer University of North Dakota
Adiabatic Wet Bulb Temperature Td Prof. Fred Remer University of North Dakota Tw T
Wet Bulb Potential Temperature (qw ) l 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. Prof. Fred Remer University of North Dakota
Prof. Fred Remer University of North Dakota
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