Phase Changes and Latent Heat Gas Solid Liquid

  • Slides: 95
Download presentation
Phase Changes and Latent Heat Gas Solid Liquid Where’s the heat? Prof. Fred Remer

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,

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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)

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)

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

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

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

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 -.

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

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

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

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

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

Three Dimensional Phase Diagram Prof. Fred Remer University of North Dakota

Phase Change l Liquid Water Molecule – Hydrogen Bonds – Shearing Energy too great

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 Ice – Volume Increases Prof. Fred Remer University of North Dakota

Phase Change l Heat is absorbed or released during the phase changes Gas Liquid

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

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

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

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)

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

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

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.

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

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.

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

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

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

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

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 +

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.

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

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

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

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

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

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

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

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

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

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 Substitute Prof. Fred Remer University of North Dakota into

Variation of Latent Heat l Another repressed memory. . . Prof. Fred Remer University

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 –

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.

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

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

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

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

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

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

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

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

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

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

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

Prof. Fred Remer University of North Dakota