Thermodynamics M. D. Eastin Phase of Water and Latent Heats We must begin to account for the thermodynamics of water Our atmosphere contains dry air and water vapor Clouds contain dry air, water vapor, liquid water, and ice
Jan 12, 2016
Thermodynamics M. D. Eastin
Phase of Water and Latent Heats
We must begin to account for the thermodynamics of water
Our atmosphere contains dry air and water vaporClouds contain dry air, water vapor, liquid water, and ice
Thermodynamics M. D. Eastin
Outline:
Review of Systems
Thermodynamic Properties of Water Multiple phases Water in Equilibrium Equilibrium Phase Changes Amagat-Andrew Diagrams
Latent Heats for Equilibrium Phase Changes
Phase of Water and Latent Heats
Thermodynamics M. D. Eastin
Homogeneous Systems:
• Comprised of a single component
• Oxygen gas• Dry air• Water vapor
• Each state variable (p, T, V, m) has the same value at all locations within the system
Review of Systems
Thermodynamics M. D. Eastin
• Thus far we have worked exclusively a homogeneous (dry air only) closed system (no mass exchange, but some energy exchange)
• So far, our versions of the Ideal gas law and the first and second laws are only applicable to dry air
• What about water vapor?
• What about the combination of dry air and water vapor?
• What about the combination of dry air, water vapor, and liquid/ice water?
Review of Systems
Dry Air
ClosedSystem
p, T, V, m, Rd
TRpα d
pd dTcdq v
T
dqds rev
Thermodynamics M. D. Eastin
Heterogeneous Systems:
• Comprised of a single component in multiple phases or multiple components in multiple phases
• Water (vapor, liquid, ice)
• Each component or phase must be defined by its own set of state variables
Review of Systems
Water VaporPv, Tv, Vv, mv
Liquid WaterPw, Tw, Vw, mw
Ice WaterPi, Ti, Vi, mi
Thermodynamics M. D. Eastin
• Our atmosphere is a heterogeneous closed system consisting of multiple sub-systems
• Very complex…we come back to it later
Review of Systems
Water Vapor
pv, Tv, Vv, mv, Rv
Open sub-system
Ice Waterpi, Ti, Vi, mi
Open sub-system
Dry Air(gas)
p, T, V, md, Rd
Closed sub-system
Liquid Waterpw, Tw, Vw, mw
Open sub-system
Energy Exchange
Mass Exchange
Thermodynamics M. D. Eastin
• For now, let’s focus our attention on the one component heterogeneous system “water” comprised of vapor and one other phase (liquid or ice)
Review of Systems
Water Vapor
pv, Tv, Vv, mv, Rv
Open sub-system
Ice Waterpi, Ti, Vi, mi
Open sub-system
Dry Air(gas)
p, T, V, md, Rd
Closed sub-system
Liquid Waterpw, Tw, Vw, mw
Open sub-system
Energy Exchange
Mass Exchange
Thermodynamics M. D. Eastin
Single Gas Phase (Water Vapor):
• Can be treated like an ideal gas when it exists in the absence of liquid water or ice (i.e. like a homogeneous closed system):
Thermodynamic Properties of Water
vvvv TRρp
pv = Partial pressure of water vapor (called vapor pressure)
ρv = Density of water vapor (or vapor density) ( The mass of the H2O molecules ) ( per unit volume ) = mv/Vv
Tv = Temperature of the water vapor
Rv = Gas constant for water vapor ( Based on the mean molecular weights ) ( of the constituents in water vapor ) = 461 J / kg K
Thermodynamics M. D. Eastin
Single Gas Phase (Water Vapor):
• When only water vapor is present, we can apply the first and second laws of thermodynamics just like we did for parcels of dry air
Thermodynamic Properties of Water
pd dTcdq v
T
dqds rev
vvvv TRρp
Thermodynamics M. D. Eastin
Multiple Phases:
• Can NOT be treated like an ideal gas when water vapor co-exists with either liquid water, ice, or both:
• This is because the two sub-systems can exchange mass between each other when an equilibrium exists
• This violates the Ideal Gas Law
Thermodynamic Properties of Water
Water Vapor
pv, Tv, Vv, mv, Rv
Open sub-system
Liquid Waterpw, Tw, Vw, mw
Open sub-system
vvvv TRρp wwww TRρp
Thermodynamics M. D. Eastin
Multiple Phases:
• When an equilibrium exists, the thermodynamic properties of each phase are equal:
Water in Equilibrium
pw, Tw
pv, Tv
Vapor and Liquid Vapor and Ice
pv, Tv
pi, Ti
wv pp
wv TT iv TT iv pp
Thermodynamics M. D. Eastin
An Example: Saturation
•Assume we have a parcel of dry air located above liquid water•Closed system
•Air is initially “unsaturated”•System is not at equilibrium
Water in Equilibrium
Dry Air(no water)
Liquid Water
Thermodynamics M. D. Eastin
An Example: Saturation
• After a short time…
• Molecules in the liquid are in constant motion (have kinetic energy)
• The motions are “random”, so some molecules are colliding with each other
• Some molecules near the surface gain velocity (or kinetic energy) through collisions
• Fast moving parcels (with a lot of kinetic energy) leave the liquid water at the top surface → vaporization
Water in Equilibrium
Thermodynamics M. D. Eastin
An Example: Saturation
• Soon there are a lot of water molecules in the air (in vapor form)…
• The water molecules in the air make collisions as well
• Some collisions result in slower moving (or lower kinetic energy) molecules
• The slower water molecules return to the water surface → condensation
Water in Equilibrium
Thermodynamics M. D. Eastin
An Example: Saturation
Eventually, the rate of condensation equals the rate of evaporation
Rate of Rate of Condensation = Evaporation
We have reached “Equilibrium”
Water in Equilibrium
Thermodynamics M. D. Eastin
Three Standard Equilibrium States:
Vaporization: Gas ↔ Liquid
Fusion: Liquid ↔ Ice
Sublimation: Gas ↔ Solid
• Each of these equilibrium states occur at certain temperatures and pressures
• Thus we can construct an equilibrium phase change graph for water
Water in Equilibrium
Sublimatio
n
Fus
ion
Vap
oriz
atio
n
T
C
T (ºC)
p (mb)
3741000
6.11
1013
221000
Liquid
Vapor
Solid
Thermodynamics M. D. Eastin
One Unique Equilibrium State:
• It is possible for all three phases to co-exist in an equilibrium at a single temperature and pressure
• Called the Triple Point
Water in Equilibrium
iwv ppp
iwv TTT
mb 6.11p
K273.16T
Sublimatio
n
Fus
ion
Vap
oriz
atio
n
T
C
T (ºC)
p (mb)
3741000
6.11
1013
221000
Liquid
Vapor
Solid
Thermodynamics M. D. Eastin
Critical Point:
• Thermodynamic state in which liquid and gas phases can co-exist in equilibrium at the highest possible temperature
• Above this temperature, water can NOT exist in the liquid phase
Other Atmospheric Gases:
Water in Equilibrium
mb 221,000pc
C374Tc
Sublimatio
n
Fus
ion
Vap
oriz
atio
n
T
C
T (ºC)
p (mb)
3741000
6.11
1013
221000
Liquid
Vapor
Solid
C119TO c2
C147TN c2
Thermodynamics M. D. Eastin
Equilibrium Phase Changes on P-V Diagrams:
Amagat-Andrews Diagram
T
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquidand
Vapor
Solidand
Vapor
Tc = 374ºC
T1
6.11
221,000
Thermodynamics M. D. Eastin
Equilibrium Phase Changes on P-V Diagrams:
Vapor Phase (A → B)
• Behaves like an ideal gas
• Decrease in volume• Increase in pressure• Heat Removed
Amagat-Andrews Diagram
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquidand
Vapor
Solidand
Vapor
Tc =374ºC
T1
6.11
221,000
T
A
B
vvvv TRρp
Thermodynamics M. D. Eastin
Equilibrium Phase Changes on P-V Diagrams:
Liquid and Vapor Phase (B → B’)
• Small change in volume causes condensation
• Some liquid water begins to form
• No longer behaves like an ideal gas
Amagat-Andrews Diagram
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquidand
Vapor
Solidand
Vapor
Tc =374ºC
T1
6.11
221,000
T
B’ B
Thermodynamics M. D. Eastin
Equilibrium Phase Changes on P-V Diagrams:
Liquid and Vapor Phase (B’ → B”)
• Condensation occurs due to a decrease in volume
• Constant temperature• Constant pressure
• Water vapor pressure is at equilibrium
Amagat-Andrews Diagram
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquidand
Vapor
Solidand
Vapor
Tc =374ºC
T1
6.11
221,000
T
B’B”
Thermodynamics M. D. Eastin
Equilibrium Phase Changes on P-V Diagrams:
Liquid and Vapor Phase (B” → C)
• All the vapor has condensed into liquid water
Amagat-Andrews Diagram
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquidand
Vapor
Solidand
Vapor
Tc =374ºC
T1
6.11
221,000
T
C B”
Thermodynamics M. D. Eastin
Equilibrium Phase Changes on P-V Diagrams:
Liquid Phase (C → D)
• Small changes in volume produce large increases in pressure
• Liquid water is virtually incompressible
Amagat-Andrews Diagram
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquidand
Vapor
Solidand
Vapor
Tc =374ºC
T1
6.11
221,000
T
C
D
Thermodynamics M. D. Eastin
Amagat-Andrews Diagram
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Tc =374ºC
T1
6.11
221,000
T
Equilibrium Phase-Change Range:
• The range of volumes for which equilibrium occurs decreases with increasing temperature
Thermodynamics M. D. Eastin
Critical Point:
• Maximum temperature at which condensation (or vaporization) can occur
• Water vapor obeys the Ideal Gas Law at higher temperatures
Amagat-Andrews Diagram
C374Tc
mb 221,000pc
C
V
P(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Tc =374ºC
T1
6.11
221,000
T
Solidand
Vapor
Liquidand
Vapor
Thermodynamics M. D. Eastin
Homogeneous System:
• Vapor only• Behaves like Ideal Gas
Isobaric Process
• Heat (dQ) added or removed from the system• Temperature changes• Volume changes
Latent Heats during Phase Changes
Vdp dTmcdQ p
dTmcdQ p
vvvv TRρp
p
V
273K 373K
dQ
Thermodynamics M. D. Eastin
Heterogeneous System:
• Liquid and Vapor
Isobaric Process
• Heat (dQ) added or removed from the system• Temperature constant• Volume changes
Latent Heats during Phase Changes
C
V
P(mb)
Vapor
Solid
Tt
Liquid
Tc
T1
T
dQ
dQ
dQ
Thermodynamics M. D. Eastin
Definition of Latent Heat (L):
• Heat absorbed (or given away) during an isobaric and isothermal phase change
• The heat is needed to form (or (results from the breaking of) the molecular bonds that hold water molecules together
Latent Heats during Phase Changes
C
V
P(mb)
Vapor
Solid
Tt
Liquid
Tc
T1
T
dQ
dQ
dQ
dQ L
Thermodynamics M. D. Eastin
Definition of Latent Heat (L):
• Heat absorbed (or given away) during an isobaric and isothermal phase change
• Magnitude varies with temperature
• However, the range of variation is very small for the range of pressures and temperatures observed in the troposphere
• Assumed constant in practice
Latent Heats during Phase Changes
C
V
P(mb)
Vapor
Solid
Tt
Liquid
Tc
T1
T
L
L
L
constantdQ L
Thermodynamics M. D. Eastin
The Different Latent Heats:
Latent Heats during Phase Changes
FusionFusion(L(Lf f or lor lff))
SublimationSublimation(L(Ls s or lor lss))
VaporizationVaporizationCondensation Condensation
(L(Lv v or lor lvv))
SolidSolidLiquidLiquid
GasGas
Values for lv, lf, and ls are given in Table A.3 of the Appendix as a function of temperature
Thermodynamics M. D. Eastin
Heat is Absorbed (dQ > 0):
Latent Heats during Phase Changes
FusionFusion(L(Lf f or lor lff))
SublimationSublimation(L(Ls s or lor lss))
VaporizationVaporizationCondensation Condensation
(L(Lv v or lor lvv))
SolidSolidLiquidLiquid
GasGas
Thermodynamics M. D. Eastin
Heat is Released (dQ < 0):
Latent Heats during Phase Changes
FusionFusion(L(Lf f or lor lff))
SublimationSublimation(L(Ls s or lor lss))
VaporizationVaporizationCondensation Condensation
(L(Lv v or lor lvv))
SolidSolidLiquidLiquid
GasGas
Thermodynamics M. D. Eastin
Summary:
• Review of Systems
• Thermodynamic Properties of Water• Multiple phases• Water in Equilibrium• Equilibrium Phase Changes• Amagat-Andrew Diagrams
• Latent Heats for Equilibrium Phase Changes
Phase of Water and Latent Heats
Thermodynamics M. D. Eastin
ReferencesPetty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp.
Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp. Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp.