The document discusses the phases of water and latent heats during phase changes. It describes water as existing in vapor, liquid, and solid phases. Equilibrium occurs when the vapor pressure of water equals the partial pressure of water vapor in air. The triple point is where vapor, liquid, and solid phases coexist at the same temperature and pressure. Latent heats refer to the heat absorbed or released during phase changes like vaporization, condensation, fusion, and sublimation without a change in temperature.

1. Phase of Water and Latent Heats
Phases of Pure Substances
Part-8

2. Our atmosphere contains dry air and water vapor
Clouds contain dry air, water vapor, liquid water, and ice
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

3. • 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
Closed
System
P, T, V, m, Rd
dPV R T=
vdQ c dT PdV= +
revdQ
dS
T
≥

4. 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 Vapor
Pv, Tv, Vv, mv
Liquid Water
Pw, Tw, Vw, mw
Ice Water
Pi, Ti, Vi, mi
• For now, let’s focus our attention on the one component heterogeneous
system “water” comprised of vapor and one other phase (liquid or ice)

5. • 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 Water
Pi, Ti, Vi, mi
Open sub-system
Dry Air
(gas)
P, T, V, md, Rd
Closed sub-system
Liquid Water
Pw, Tw, Vw, mw
Open sub-system
Energy Exchange
Mass Exchange

6. 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
v v v vPρ R T=
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)
ρv = 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

7. 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 dry air
vdQ c dT PdV= + revdQ
dS
T
≥v v v vPρ R T=
Multiple Phases:
• Can NOT be treated like an ideal gas when water vapor
co-exists with either liquid water, ice, or both:
Water Vapor
Pv, Tv, Vv, mv, Rv
Open sub-system
Liquid Water
Pw, Tw, Vw, mw
Open sub-system
v v v vPρ R T= w w w wPρ R T=
•This is because the two sub-systems
can exchange mass between each
other when an equilibrium exists
This violates the Ideal Gas Law

8. Multiple Phases:
• When an equilibrium exists, the thermodynamic properties
of each phase are equal:
Pw, Tw
Pv, Tv
Vapor and Liquid Vapor and Ice
Pv, Tv
Pi, Ti
v wP P=
wv TT = iv TT =
v iP P=

9. 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
• 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

10. • 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, continue…
 Eventually, the rate of condensation
equals the rate of evaporation
Rate of Rate of
Condensation = Evaporation
We have reached “Equilibrium”

11. Three Standard Equilibrium States:
Vaporization: Liquid →Gas
Fusion: Ice → Liquid
Sublimation: Solid → Gas
Water in Equilibrium
Sublim
ation
Fusion
Vaporization
T
C
T (ºC)
p (mb)
3741000
6.11
1013
221000
Liquid
Vapor
Solid
•Each of these equilibrium states occur at certain temperatures and pressures
• Thus we can construct an equilibrium phase change graph for water

12. Sublimation:
It is the conversion between the solid and the gaseous phases
of matter, with no intermediate liquid stage.
The triple point
is where all
three phases
are in
equilibrium

13. The generic phase diagram of a substance in
the P-T coordinates
Every point of this diagram is an equilibrium
state
Different states of the system in equilibrium
are called phases.
The lines dividing different phases are called
the coexistence curves.
Along these curves, the phases coexist in
equilibrium, and the system is
macroscopically inhomogeneous.
At the triple point : all three phases coexist at
(Ttr , Ptr).
The guiding principle is the minimization of
the Gibbs free energy in equilibrium for all
systems, including the multi-phase ones.

15. 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 (T)
v w iP P P= = iwv TTT ==P 6.11 mb= K273.16T =
Sublim
ation
Fusion
Vaporization
T
C
T (ºC)
p (mb)
3741000
6.11
1013
221000
Liquid
Vapor
Solid
Critical Point (C)
• 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
C374Tc

= cP 221,000 mb=
Other Atmospheric Gases:
C119TO c2

−=→ C147TN c2

−=→

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

17. 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
Liquid
and
Vapor
Solid
and
Vapor
Tc =
374ºC
T1
6.11
221,000
T
B’ B
Equilibrium Phase Changes on P-V Diagrams:Amagat-Andrews Diagram

18. 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
Liquid
and
Vapor
Solid
and
Vapor
Tc =
374ºC
T1
6.11
221,000
T
B’B”
Equilibrium Phase Changes on P-V Diagrams:Amagat-Andrews Diagram

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

20. Liquid Phase (C → D)
• Small changes in volume
produce large increases
in pressure
• Liquid water is virtually
incompressible
C
V
P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Liquid
and
Vapor
Solid
and
Vapor
Tc =
374ºC
T1
6.11
221,000
T
C
D
Equilibrium Phase Changes on P-V Diagrams:Amagat-Andrews Diagram

21. C
V
P
(mb)
Vapor
Solid
Tt = 0ºC
Liquid
Tc =
374ºC
T1
6.11
221,000
T
• The range of volumes for which equilibrium occurs decreases with
increasing temperature
Equilibrium Phase Changes on P-V Diagrams:Amagat-Andrews Diagram
Critical Point:
• Maximum temperature at which
condensation (or vaporization) can
occur
• Water vapor obeys the Ideal Gas Law
at higher temperatures
C374Tc

=
cP 221,000 mb=

22. 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
pdQ mc dT VdP= +
dTmcdQ p=
vvvv TRρp =
p
V
273K 373K
dQ

23. Heat and Phase Change
When two phases coexist, the temperature remains the same even if a small
amount of heat is added. Instead of raising the temperature, the heat goes into
changing the phase of the material – melting ice, for example.

24. Latent HeatThe heat required to convert
from one phase to another is
called the latent heat.
The latent heat, L, is the heat that
must be added to or removed
from one kilogram of a substance
to convert it from one phase to
another.
During the conversion process,
the temperature of the system
remains constant.
The latent heat of fusion is the
heat needed to go from solid to
liquid;
the latent heat of vaporization
from liquid to gas.

25. Example 1: Which will cause more severe burns to your skin: 100°C water or
100°C steam?
a) Water b) steam c) both the same d) it depends...
Example 2 :You put 1 kg of ice at 0°C together with 1 kg of water at 50°C.
What is the final temperature?
LF = 80 cal/g
cwater = 1 cal/g °C
a) 0°C b) between 0°C and 50°C c) 50°C d) greater than 50°C

26. Although the water is indeed hot, it releases only 1 cal/1 cal/gg of heat as it cools. The
steam, however, first has to undergo a phase changephase change into water and that process
releases 540 cal/g540 cal/g, which is a very large amount of heat. That immense release of
heat is what makes steam burns so dangerous.
Which will cause more severe burns to your
skin: 100°C water or 100°C steam?
a) water
b) steam
c) both the same
d) it depends...

27. How much heat is needed to melt the ice?
QQ == mLmLff = (1000= (1000 gg)) ×× (80 cal/(80 cal/gg) = 80,000 cal) = 80,000 cal
How much heat can the water deliver by cooling from 50°°C to 0°°C?
QQ == ccwaterwater mm ∆∆TT = (1 cal/= (1 cal/gg °°C)C) ×× (1000(1000 gg)) ×× (50(50°°C) = 50,000 calC) = 50,000 cal
Thus, there is not enough heat available to melt all the ice!!
Question 11.8Question 11.8 Water and IceWater and Ice
You put 1 kg of ice at 0°C
together with 1 kg of water at
50°C. What is the final
temperature?
LF = 80 cal/g
cwater = 1 cal/g °C
a) 0°C
b) between 0°C and 50°C
c) 50°C
d) greater than 50°C

28. 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
•The heat is needed to form (or (results from
the breaking of) the molecular bonds that
hold water molecules together
dQL =
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 constantdQL ==

29. The Different Latent Heats:
Latent Heats during Phase Changes
FusionFusion
(L(Lff or lor lff))
SublimationSublimation
(L(Lss or lor lss))
VaporizationVaporization
CondensationCondensation
(L(Lvv or lor lvv))
SolidSolidLiquidLiquid
GasGas
Values for lv, lf, and ls
are tabulated in some texts

30. Heat is Absorbed (dQ > 0):
FusionFusion
(L(Lff or lor lff))
SublimationSublimation
(L(Lss or lor lss))
VaporizationVaporization
CondensationCondensation
(L(Lvv or lor lvv))
SolidSolidLiquidLiquid
GasGas
Latent Heats during Phase Changes

31. Heat is Released (dQ < 0):
FusionFusion
(L(Lff or lor lff))
SublimationSublimation
(L(Lss or lor lss))
VaporizationVaporization
CondensationCondensation
(L(Lvv or lor lvv))
SolidSolidLiquidLiquid
GasGas
Latent Heats during Phase Changes