1. 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
Thermodynamics
M. D. Eastin

2. Phase of Water and Latent Heats
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
Thermodynamics
M. D. Eastin

3. Review of Systems 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
Thermodynamics
M. D. Eastin

4. Review of Systems Thus far we have worked exclusively with
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?
of dry air, water vapor, and
liquid/ice water?
Dry Air
Closed
System
p, T, V, m, Rd
Thermodynamics
M. D. Eastin

5. Review of Systems 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
Water Vapor
Pv, Tv, Vv, mv
Ice Water
Pi, Ti, Vi, mi
Liquid Water
Pw, Tw, Vw, mw
Thermodynamics
M. D. Eastin

6. Review of Systems Our atmosphere is a heterogeneous
closed system consisting of multiple
sub-systems
Very complex…we come back to it later
Water Vapor
pv, Tv, Vv, mv, Rv
Open sub-system
Ice Water
pi, Ti, Vi, mi
Dry Air
(gas)
p, T, V, md, Rd
Closed sub-system
Liquid Water
pw, Tw, Vw, mw
Energy Exchange
Mass Exchange
Thermodynamics
M. D. Eastin

7. Review of Systems For now, let’s focus our attention on
the one component heterogeneous
system “water” comprised of vapor
and one other phase (liquid or ice)
Water Vapor
pv, Tv, Vv, mv, Rv
Open sub-system
Ice Water
pi, Ti, Vi, mi
Dry Air
(gas)
p, T, V, md, Rd
Closed sub-system
Liquid Water
pw, Tw, Vw, mw
Energy Exchange
Mass Exchange
Thermodynamics
M. D. Eastin

8. Thermodynamic Properties of Water
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):
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

9. Thermodynamic Properties of Water
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
Thermodynamics
M. D. Eastin

10. Thermodynamic Properties of Water
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
Water Vapor
pv, Tv, Vv, mv, Rv
Open sub-system
Liquid Water
pw, Tw, Vw, mw
Thermodynamics
M. D. Eastin

11. Water in Equilibrium pv, Tv pv, Tv pi, Ti pw, Tw Multiple Phases:
When an equilibrium exists, the thermodynamic properties
of each phase are equal:
Vapor and Liquid
Vapor and Ice
pv, Tv
pv, Tv
pi, Ti
pw, Tw
Thermodynamics
M. D. Eastin

12. Water in Equilibrium 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
Dry Air
(no water)
Liquid Water
Thermodynamics
M. D. Eastin

13. Water in Equilibrium 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
Thermodynamics
M. D. Eastin

14. Water in Equilibrium 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
Thermodynamics
M. D. Eastin

15. Water in Equilibrium An Example: Saturation
Eventually, the rate of condensation
equals the rate of evaporation
Rate of Rate of
Condensation = Evaporation
We have reached “Equilibrium”
Thermodynamics
M. D. Eastin

16. Water in Equilibrium 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
Sublimation
Fusion
Vaporization T C
T (ºC)
p (mb)
374
100
6.11
1013
221000
Liquid
Vapor
Solid
Thermodynamics
M. D. Eastin

17. Water in Equilibrium 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
Sublimation
Fusion
Vaporization T C
T (ºC)
p (mb)
374
100
6.11
1013
221000
Liquid
Vapor
Solid
Thermodynamics
M. D. Eastin

18. Water in Equilibrium 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:
Sublimation
Fusion
Vaporization T C
T (ºC)
p (mb)
374
100
6.11
1013
221000
Liquid
Vapor
Solid
Thermodynamics
M. D. Eastin

19. Amagat-Andrews Diagram
Equilibrium Phase Changes on P-V Diagrams: T C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
and
Tc = 374ºC T1
6.11
221,000
Thermodynamics
M. D. Eastin

20. Amagat-Andrews Diagram
Equilibrium Phase Changes on P-V Diagrams:
Vapor Phase (A → B)
Behaves like an ideal gas
Decrease in volume
Increase in pressure
Heat Removed C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
and
Tc =
374ºC T1
6.11
221,000 T A B
Thermodynamics
M. D. Eastin

21. Amagat-Andrews Diagram
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 C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
and
Tc =
374ºC T1
6.11
221,000 T B’ B
Thermodynamics
M. D. Eastin

22. Amagat-Andrews Diagram
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 C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
and
Tc =
374ºC T1
6.11
221,000 T B’ B”
Thermodynamics
M. D. Eastin

23. Amagat-Andrews Diagram
Equilibrium Phase Changes on P-V Diagrams:
Liquid and Vapor Phase (B” → C)
All the vapor has condensed
into liquid water C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
and
Tc =
374ºC T1
6.11
221,000 T B”
Thermodynamics
M. D. Eastin

24. Amagat-Andrews Diagram
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 P
(mb)
Liquid C
221,000 D
Tc =
374ºC
Vapor C
Liquid
and
Vapor T1
Solid T
6.11
Solid
and
Vapor
Tt = 0ºC V
Thermodynamics
M. D. Eastin

25. Amagat-Andrews Diagram
Equilibrium Phase-Change Range:
The range of volumes for
which equilibrium occurs
decreases with increasing
temperature C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Tc =
374ºC T1
6.11
221,000 T
Thermodynamics
M. D. Eastin

26. Amagat-Andrews Diagram
Critical Point:
Maximum temperature
at which condensation
(or vaporization) can
occur
Water vapor obeys the
Ideal Gas Law at
higher temperatures C V P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Tc =
374ºC T1
6.11
221,000 T
and
Thermodynamics
M. D. Eastin

27. Latent Heats during Phase Changes
Homogeneous System:
Vapor only
Behaves like Ideal Gas
Isobaric Process
Heat (dQ) added or removed
from the system
Temperature changes
Volume changes p V
273K
373K dQ
Thermodynamics
M. D. Eastin

28. Latent Heats during Phase Changes
Heterogeneous System:
Liquid and Vapor
Isobaric Process
Heat (dQ) added or removed
from the system
Temperature constant
Volume changes C V P
(mb)
Vapor
Solid Tt
Liquid Tc T1 T dQ
Thermodynamics
M. D. Eastin

29. Latent Heats during Phase Changes
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 C V P
(mb)
Vapor
Solid Tt
Liquid Tc T1 T dQ
Thermodynamics
M. D. Eastin

30. Latent Heats during Phase Changes
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 C V P
(mb)
Vapor
Solid Tt
Liquid Tc T1 T L
Thermodynamics
M. D. Eastin

31. Latent Heats during Phase Changes
The Different Latent Heats:
Fusion
(Lf or lf)
Sublimation
(Ls or ls)
Vaporization
Condensation
(Lv or lv)
Solid
Liquid
Gas
Values for lv, lf, and ls
are given in Table A.3
of the Appendix as a
function of temperature
Thermodynamics
M. D. Eastin

32. Latent Heats during Phase Changes
Heat is Absorbed (dQ > 0):
Gas
Vaporization
Condensation
(Lv or lv)
Sublimation
(Ls or ls)
Liquid
Solid
Fusion
(Lf or lf)
Thermodynamics
M. D. Eastin

33. Latent Heats during Phase Changes
Heat is Released (dQ < 0):
Gas
Vaporization
Condensation
(Lv or lv)
Sublimation
(Ls or ls)
Liquid
Solid
Fusion
(Lf or lf)
Thermodynamics
M. D. Eastin

34. Phase of Water and Latent Heats
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
Thermodynamics
M. D. Eastin

35. References Thermodynamics M. D. Eastin
Petty, 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.
Thermodynamics
M. D. Eastin