Thermodynamics lecture 4

BITS PilaniBITS PilaniPilani Campus

Properties of a pure substance

Pure Substance

The pure substance is one that haspa homogeneous and invariablechemical composition.p

A pure substance may exist in manyA pure substance may exist in manyphases, but the chemical compositionis same in all the phasesis same in all the phases.

BITS Pilani, Pilani Campus

BITS PilaniBITS PilaniPilani Campus

VaporVapor LiquidLiquid Solid Phase Solid Phase VaporVapor--LiquidLiquid--Solid Phase Solid Phase Equilibrium in a Pure SubstanceEquilibrium in a Pure Substance

Phase Equilibrium in a Pure Substance

Saturation temperature means the temperature at

Substance

which change of phase takes place at a given pressure.

Saturation Pressure means the pressure at whichSaturation Pressure means the pressure at whichchange of phase takes place at a given temperature.



Latent heat: the amount of energy absorbed or

Substance

released during a phase-change process.

Latent heat of fusion: the amount of energyabsorbed during meltingabsorbed during melting.

Latent heat of vaporization: the amount of energyabsorbed during vaporization.


Constant pressure change from solid to vapor phase for pure substance (substance that contracts on freezing)(substance that contracts on freezing)

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Phase Equilibrium in a Pure Substanceq


Phase Equilibrium in a Pure S b t

Sub-cooled Solid (1)Substance

( )Saturated Solid (2)Sub cooled / compressed liquid (betweenSub-cooled / compressed liquid (between

3 & 4) S t t d li id (3 t S L ilib iSaturated liquid (3 - w.r.t. S-L equilibrium,

4 - w.r.t. L - G equilibrium)


Phase Equilibrium in a Pure S b t

Saturated vapour (5) Substance

p ( )Saturation temp(2 - S; 3 - L w.r.t. S-L

equilibrium; q ;4 – L, 5 - G w.r.t. L - G equilibrium)

Liquid vapour mixture (between 4 andLiquid vapour mixture (between 4 and 5)

Superheated vapour (beyond 5)Superheated vapour (beyond 5) Saturation pressure


Phase Equilibrium in a Pure Substanceq

Superheated vapour Saturated liquid(4)

Saturation temp Liquid vapour mixture(4-5)

Saturated liquid(4)

Saturated Solid (2)p

Sub cooled / compressed liquid(3 4)

Saturated vapour(5)

Sub-cooled / compressed liquid(3-4)

Saturated liquid(3)


Sub-cooled Solid Solid –Liquid Mixture(2-3)

Saturated Liquid lineLiquid line

Critical Point

Saturated Vapour line

Triple LineSaturated Solid line

Saturated Solid line

Saturated Liquid lineP-v-T surface

of a

Liquid line

substance that contractson freezing.

Saturated Vapour line Triple Line

Constant pressure change from solid to vapor h f b t phase for pure substance

(substance that expands on freezing eg.water)


Constant pressure change from solid to vapor phase for pure substance (water)vapor phase for pure substance (water)


P-v-T surface su aceof a substance substa cethat expands on freezing.g

Saturated Solid line

Saturated Liquid lineLiquid line

P-v-T surface of a substance that contracts on freezing.

Saturated Vapour line Triple Line

The Triple Point …

The three lines that met at the triple point, they h d f

p

represent the conditions of:

l l d l d l bFusion line - Solid-liquid equilibrium Vaporization line – Liquid-vapor equilibriumSublimation line – Solid-vapor equilibrium

Where all three lines meet, we have a uniquecombination of temperature and pressure where allthree phases are in equilibrium


three phases are in equilibrium.

The Triple Point …The Triple Point …


Unusual behavior of water …

The phase diagram shows that waterld fi f f i iwould first freeze to form ice as it

crosses into the solid area.

With further decreasing pressure, iceld th bli t iwould them sublime to give vapor.

S i h d iSo with decreasing pressure,Liquid Solid Vapor


Unusual behavior of water …


The Critical Point

The liquid vapor equilibrium curve has an upperlimit labeled as C This is known as the Criticallimit, labeled as C. This is known as the CriticalPoint.

Above the critical temperature, it is impossible tocondense a gas into a liquid just by increasingpressurepressure.

The critical temperature varies from substance topsubstance.



If for given pressure,


The temperature of liquid is lower thansaturation temperature, it is called asubcooled liquid (T < TS) or a compressedsubcooled liquid (T < TS) or a compressedliquid (P > PS).

A liquid that is not about to vaporize.

If for given pressure, the temperature of vaporis greater than saturation temperature it isis greater than saturation temperature, it iscalled a superheated vapor.

A vapor that is not about to condense


Phase Equilibrium in a Pure Substance …

At saturation temperature and

Phase Equilibrium in a Pure Substance …

At saturation temperature andpressure, if a substance exists asliquid it is called saturated liquidliquid, it is called saturated liquid.

At saturation temperature andpressure, if a substance exists aspressure, if a substance exists asvapor, it is called saturated vapor.


Liquid + vapor region


Compressed liquid region


Superheated vapor region


Supercritical fluid region


Gibbs Phase Rule

The Phase Rule describes the possiblenumber of degrees of freedom in anumber of degrees of freedom in a(closed) system at equilibrium, in termsof the number of separate phases andthe number of chemical constituents inthe number of chemical constituents inthe system.

The Degrees of Freedom [F] is thenumber of independent intensivevariables that need to be specified invariables that need to be specified invalue to fully determine the state of thesystem.


Gibbs Phase Rule

Gibbs Phase Rule:F = C - P + 2

Where P: The number of phases C: The Chemical Constituents

For Example: A system with oneFor Example: A system with onecomponent and one phase has twodegrees of freedom: temperature andpressure say can be variedpressure, say, can be variedindependently.


Gibbs Phase Rule

For pure substance (C=1)p ( )F = 1 + 2 – P = 3 – PF = 3 – PF 3 P

For P = 1 F = 2 ( P & T independent)

For P = 2, F = 1( P & T dependent)

For P = 3, F = 0 ( Triple Point)


, ( p )

Example 1

Determine whether water at each of the following

p

gstates is a compressed liquid, a superheatedvapor, or a mixture of saturated liquid andvapor.

a. 10 MPa, 0.003 m3/kgO 3b. 200 OC, 0.1 m3/kg

c. 1 MPa, 190 OCd. 10 kPa, 10 OC

We consult Table B.1.1 if T is given, and Table


B.1.2 if P is given.

Example 1: Solution

a. 10 MPa, 0.003 m3/kggvf = 0.001452, vg = 0.01803 m3/kg. So it is a mixture of liquid and vapor.

b. 200 OC, 0.1 m3/kgv < vg = 0.12736 m3/kg, so it is two phase g g pmixture

c. 1 MPa, 190 OCT > Tsat = 179.91 OC, so it is superheated vapor.

d. 10 kPa, 10 OC


P > Pg = 1.2276 kPa, so it is compressed liquid.

Example 2

Give the phase and specific volume for followingstates:

a. Water at T = 275 OC, P = 5 MPa

b. Water at T = -2 OC, P = 100 kPa

c. Ammonia at T = 170 OC, P = 600 kPa


,

Example 2

Give the phase and specific volume forGive the phase and specific volume forfollowing states:a. Water at T = 275 OC, P = 5 MPa,

Consult Table B.1.1 or B.1.2P t = 5.94 MPa, so we have superheatedPsat 5.94 MPa, so we have superheated vapor. v = 0.04141 m3/kg0 0 3/ g


Example 2

b W t t T 2 OC P 100 kPb. Water at T = -2 OC, P = 100 kPaConsult Table B.1.5Psat = 0.518 kPa, so we have compressed solid. v = vl = 0.0010904 m3/kg


Example 2

A i t T 170 OC P 600 kPc. Ammonia at T = 170 OC, P = 600 kPaConsult Table B.2.2 T > Tc and P<Pc, so we have superheated vapor. pv = (0.34699 + 0.36389)/2 = 0.3554 m3/kg


Example 3

b. Ammonia at T = 170 OC, P = 600 kPaaConsult Table B.2.2

T > Tc and P<Pc, so we have s perheated aporsuperheated vapor.v = (0.34699 + 0.36389)/2 = 0.3554 ( )m3/kg

Thermodynamics lecture 4

Documents

Transcript of Thermodynamics lecture 4