Thermodynamic, part 7

Phase of Water and Latent Heats

Phases of Pure Substances

Part-8

Our atmosphere contains dry air and water vaporClouds 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

• 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 SystemsDry Air

ClosedSystemP, T, V, m, Rd

dPV R T=

vdQ c dT PdV= +

revdQdS

T≥

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

• For now, let’s focus our attention on the one component heterogeneous system “water” comprised of vapor and one other phase (liquid or ice)

• 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


Open sub-system

Energy Exchange

Mass Exchange

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 vaporRv = Gas constant for water vapor ( Based on the mean molecular weights ) ( of the constituents in water vapor ) = 461 J / kg K

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= + revdQdS

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


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

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=

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 EquilibriumDry 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

• 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”

Three Standard Equilibrium States:

Vaporization: Liquid →Gas Fusion: Ice → Liquid Sublimation: Solid → Gas

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

•Each of these equilibrium states occur at certain temperatures and pressures• Thus we can construct an equilibrium phase change graph for water

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

The generic phase diagram of a substance in the P-T coordinates

Every point of this diagram is an equilibrium stateDifferent 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.

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 =

Sublimatio

n

Fus

ion

Vap

oriz

atio

n

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

−=→

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

LiquidandVapor

SolidandVapor

Tc =374ºC

T1

6.11

221,000

T

A

B

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

LiquidandVapor

SolidandVapor

Tc =374ºC

T1

6.11

221,000

T

B’ B


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

LiquidandVaporSolidandVapor

Tc =374ºC

T1

6.11

221,000

T

B’B”


Liquid and Vapor Phase (B” → C)

• All the vapor has condensed into liquid water

C

V

P(mb)

Vapor

Solid

Tt = 0ºC

Liquid

LiquidandVaporSolidandVapor

Tc =374ºC

T1

6.11

221,000

T

C B”


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

LiquidandVapor

SolidandVapor

Tc =374ºC

T1

6.11

221,000

T

C

D


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


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=

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

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.

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.

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

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...

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 Ice Water 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

Heterogeneous System: Liquid and VaporIsobaric 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

dQ

dQ

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

dQ L =

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 constantdQ L ==

The Different Latent Heats:


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 tabulated in some texts

Heat is Absorbed (dQ > 0):





GasGas


Heat is Released (dQ < 0):





GasGas


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Thermodynamic, part 7