Prof. Fred Remer University of North Dakota Phase Changes and Latent Heat Where’s the heat? Solid Liquid Gas

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 pp 60 – 63 l Bohren & Albrecht –pp 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 l Be able to recall from memory the definition of critical point l Be able to recall from memory the definition of triple point

Prof. Fred Remer University of North Dakota Objectives l 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

Prof. Fred Remer University of North Dakota Objectives l 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

Prof. Fred Remer University of North Dakota Objectives l 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

Prof. Fred Remer University of North Dakota Objectives l 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

Prof. Fred Remer University of North Dakota Objective l 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

Prof. Fred Remer University of North Dakota SolidLiquidGas Phase Changes l Phase change results in a transformation of the molecular structure

Prof. Fred Remer University of North Dakota T Phase Change l Temperature of substance does not change during transformation

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 l Can Occur at Various Temperatures and Equilibrium Pressures Vapor Water Water & Vapor Volume (V) Pressure (e) Ice & Vapor T1T1T1T1 Ice T2T2T2T2 T3T3T3T3 T4T4T4T4 T5T5T5T5

Prof. Fred Remer University of North Dakota Phase Change l Volume changes significantly during phase change Condensation

Prof. Fred Remer University of North Dakota Phase Change l Entropy also changes Solid LiquidGas Increasing Entropy

Prof. Fred Remer University of North Dakota Phase Change –Vapor to Ice –Water to Ice –Triple Line l The thermodynamic state at which three phases of a substance exist in equilibrium. Vapor Water Water&Vapor Volume (V) Pressure (e) Ice & Vapor 0oC0oC0oC0oC T Ice Ice & Water l Phase Change (P-V Diagram) Triple Line

Prof. Fred Remer University of North Dakota Phase Change –Triple Line l T = K l e s = mb Vapor Water Water&Vapor Volume (V) Pressure (e) Ice & Vapor 0oC0oC0oC0oC T Ice Ice & Water l Phase Change (P-V Diagram) Triple Line

Prof. Fred Remer University of North Dakota Phase Change –Vapor to Water l Critical Point (P c ) –The thermodynamic state in which liquid and gas phases of a substance coexist in equilibrium at the highest possible temperature. l Phase Change (P-V Diagram) Vapor Water Water&Vapor Volume (V) Pressure (e) Ice & Vapor 0oC0oC0oC0oC T Ice Ice & Water Critical Point

Prof. Fred Remer University of North Dakota Phase Change –Vapor to Water l Critical Point (P c ) –No liquid phase can exist at temperatures higher than the critical temperature –T c = 647 K –P c = 222,000 mb l Phase Change (P-V Diagram) Vapor Water Water&Vapor Volume (V) Pressure (e) Ice & Vapor 0oC0oC0oC0oC T Ice Ice & Water Critical Point

Prof. Fred Remer University of North Dakota Phase Change l Phase Change (P-T Diagram) Temperature Pressure Liquid eswesweswesw Gas esiesiesiesi Solid

Prof. Fred Remer University of North Dakota Phase Change l Isothermal Compression Temperature Pressure Liquid eswesweswesw Gas esiesiesiesi Solid

Prof. Fred Remer University of North Dakota Phase Change l Isobaric Cooling Temperature Pressure Liquid eswesweswesw Gas esiesiesiesi Solid

Prof. Fred Remer University of North Dakota Phase Change l Changes in Atmospheric Pressure Temperature Pressure Liquid Gas Solid o C atm -1 –Change in Freezing Point

Prof. Fred Remer University of North Dakota Phase Change l Changes in Atmospheric Pressure Temperature Pressure Liquid Gas Solid –Change in Boiling Point

Prof. Fred Remer University of North Dakota Phase Change l Critical Point Temperature Pressure Liquid Critical Point Gas esiesiesiesi Solid

Prof. Fred Remer University of North Dakota Phase Change l Triple Point Temperature Pressure Liquid Critical Point Gas 0.01 o C esiesiesiesi 6.11 mb TriplePoint Solid

Prof. Fred Remer University of North Dakota Three Dimensional Phase Diagram Ice & water Water&Vapor Vapor Water Ice & Water (hidden) Triple State Ice Temperature Specific Volume Vapor Pressure Critical Point

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

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

Prof. Fred Remer University of North Dakota Solid Liquid Gas Phase Change l Heat is absorbed or released during the phase changes

Prof. Fred Remer University of North Dakota Solid Liquid Gas Melting Sublimation Evaporation Phase Change l Heat Absorbed

Prof. Fred Remer University of North Dakota Phase Change l Heat Released Solid Liquid Gas Freezing Deposition Condensation

Prof. Fred Remer University of North Dakota Phase Change l Latent Heat –The heat required to change the molecular configuration of a substance SolidLiquidGas

Prof. Fred Remer University of North Dakota Phase Change l Latent Heat Solid Liquid Gas Fusion (l f ) Sublimation (l s ) Vaporization (l v )

Prof. Fred Remer University of North Dakota Phase Change l Latent Heat –Increase in internal energy results from the change in molecular configuration SolidLiquidGas

Prof. Fred Remer University of North Dakota Latent Heat l First Law of Thermodynamics –Internal Energy changes –Temperature is constant! –Pressure is constant –Volume changes l Work is done

Prof. Fred Remer University of North Dakota Latent Heat l Rearrange  v = specific volume of vapor  w = specific volume of liquid l For a phase change from liquid to vapor

Prof. Fred Remer University of North Dakota u v = internal energy of vapor u w = internal energy of liquid l Define the change in Internal Energy Latent Heat l Substitute l Into

Prof. Fred Remer University of North Dakota Latent Heat l Latent Heat (l v ) = 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 (l f ) l 3.34x10 5 J kg -1 –Latent Heat of Vaporization (l v ) l 2.500x10 6 J kg -1

Prof. Fred Remer University of North Dakota Latent Heat l Latent Heat of Sublimation (l s ) at 0 o C l s = l f + l v l s = 2.834x10 6 J kg -1 Temperature Pressure Liquid eswesweswesw Gas 0.01 o C esiesiesiesi Solid 6.11 mb TriplePoint

Prof. Fred Remer University of North Dakota Latent Heat l Varies with temperature Vapor Water Volume (V) Pressure (e) 0oC0oC0oC0oC T Ice dQ dQ dQ dQ

Prof. Fred Remer University of North Dakota 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 And since  w <<  v

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 c v v = 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 e s 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 c w = specific heat of liquid water

Prof. Fred Remer University of North Dakota Variation of Latent Heat l Substitute into

Prof. Fred Remer University of North Dakota 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 l Specific Heat of Vapor (at constant pressure) l Specific Heat of Liquid Water

Prof. Fred Remer University of North Dakota Latent Heat l Evaluate c pv = specific heat of vapor = 1952 J K -1 kg -1 c w = 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? l v = latent heat of K = 2.5 x 10 6 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 Summary l Specific Heat –Dry Air l Constant Volume c v = 717 J K -1 kg -1 l Constant Pressure c p = 1004 J K -1 kg -1

Prof. Fred Remer University of North Dakota Summary l Specific Heat –Water Vapor l Constant Volume –c v v = 1463 J K -1 kg -1 l Constant Pressure –c p v = 1870 J K -1 kg -1

Prof. Fred Remer University of North Dakota Summary l Specific Heat –Liquid Water (0 o C) l c w = 4218 J K -1 kg -1 l c w = 1 cal g -1 K -1 –Ice (0 o C) l c i = 2106 J K -1 kg -1

Prof. Fred Remer University of North Dakota Summary l First Law of Thermodynamics l For an isobaric process

Prof. Fred Remer University of North Dakota Summary l Latent Heat –The heat required to change the molecular configuration of a substance SolidLiquidGas

Prof. Fred Remer University of North Dakota 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 Solid Liquid Gas Fusion (l f ) Sublimation (l s ) Vaporization (l v )

Prof. Fred Remer University of North Dakota 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 l v = 2.50 x 10 6 J kg -1 – Fusion l l f = 3.34 x 10 5 J kg -1 –Sublimation l l s = x 10 6 J kg -1

Prof. Fred Remer University of North Dakota Moisture Variables l Wet-Bulb Temperature (T w ) –The temperature to which air is cooled by evaporating water into it at constant pressure until the air is saturated TwTwTwTw

Prof. Fred Remer University of North Dakota Moisture Variables l Wet Bulb Temperature (T w ) –Two methods to compute l Thermodynamic (or Isobaric) Method l Adiabatic Method

Prof. Fred Remer University of North Dakota Themodynamic Wet Bulb Temperature l Different than Dew Point Temperature TwTwTwTw TdTdTdTd

Prof. Fred Remer University of North Dakota Moisture Variables l Dew Point (T d ) –Temperature to which air must be cooled at constant pressure in order for it to become saturated with respect to liquid water TdTdTdTd

Prof. Fred Remer University of North Dakota Dew Point Temperature Temperature Pressure eseseses T atmosphere e saturation RH = 100% TdTdTdTd IsobaricCooling

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature Temperature Pressure eseseses T atmosphere eeee RH = 100% TdTdTdTd Evaporation TwTwTwTw

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 TwTwTwTw

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature l Heat Balance Heat lost by air Heat required to vaporize water = TwTwTwTw dQ dQ c p = specific heat of air c w = specific heat of water m v = mass of water that evaporates l v = latent heat of vaporization

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature TwTwTwTw c p d = specific heat of dry air c p v = specific heat of water vapor c w = specific heat of liquid water m d = mass of dry air m v = mass of water vapor

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature TwTwTwTw T TwTwTwTw w T w = wet bulb temperature T a = temperature of the air

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature TwTwTwTw T TwTwTwTw w m v sat = mass of water vapor of saturated air m vun sat = mass of water vapor of unsaturated air m vun sat - m vun sat = amount of water vapor evaporated into air

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature l Divide both sides by m d TwTwTwTw T TwTwTwTw w w sat = mixing ratio of saturated air w unsat = mixing ratio of unsaturated air

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature l As m d increases, wc p v and m w /m d decreases –Can be neglected TwTwTwTw T TwTwTwTw w

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature l Substitute for mixing ratio TwTwTwTw T TwTwTwTw w

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature l Solve for e TwTwTwTw T TwTwTwTw w

Prof. Fred Remer University of North Dakota Thermodynamic Wet Bulb Temperature l Psychrometric Equation TwTwTwTw T TwTwTwTw w l Psychrometric Constant

Prof. Fred Remer University of North Dakota TwTwTwTw T TwTwTwTw w w’ Thermodynamic Wet Bulb Temperature l Other Factors –Ventilation –Radiation –Instrumentation

Prof. Fred Remer University of North Dakota TwTwTwTw T,w s TwTwTwTw w w’ Thermodynamic Wet Bulb Temperature l Measure T & T w l e sat is a Function of T w via Claussius-Clapeyron l e is a Function of T via Claussius-Clapeyron

Prof. Fred Remer University of North Dakota 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 % Dry Bulb o F

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 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 T TdTdTdTd TwTwTwTw

Prof. Fred Remer University of North Dakota Wet Bulb Potential Temperature (  w ) 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