eso201a department of mechanical engineering...

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Department of Mechanical Engineering

Indian Institute of Technology Kanpur

Kanpur 208016

India

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Thermodynamics

Instructor: Dr. Sameer Khandekar

Tel: 7038; e-mail: [email protected]

Phase Diagrams

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Thermodynamics



Increasing the temperature isobarically

T-v diagram of

constant-pressure

phase-change

processes of a

pure substance at

various pressures

numerical values

are for water.

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Thermodynamics



Temperature - Volume diagram

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Thermodynamics



Pressure – Volume diagram

The pressure is gradually

reduced by removing the weights

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Thermodynamics



P-v-T surfacesRemembering:

(i) The State Postulate: The state of a simple

compressible substance is fixed by any two

independent, intensive properties

and

(ii) Any equation with two independent variables in

the form z = z (x, y) represents a surface

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Thermodynamics



P-v-T Surfaceof a substance

that expands on freezing.

Orthogonal projection of P-v-T

surface

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Thermodynamics



P-v-T Surfaceof a substance

that contracts on freezing.

Orthogonal projection of P-v-T

surface

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Thermodynamics



P-v diagrams

liquid + vapor

solid + vapor

Triple line

liq

uid

So

lid

+li

qu

id

so

lid

Critical point

vapor

Substances that contract on freezing

liquid + vapor

solid + vapor

Triple line

liq

uid

So

lid

+li

qu

id

so

lid

Critical point

vapor

Substances that expand on freezing

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Thermodynamics



PVT surface for ideal gases

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Thermodynamics



Phase transformationsSublimation line: Solid and Vapor

phase is in equilibrium

Fusion line: Solid and Liquid phase

is in equilibrium

Vaporization line: Liquid and Vapor

phase is in equilibrium

Triple point: All the three phases

are in equilibrium

Above critical point: No sharp

distinction in the liquid and vapor

phases

For water,

Ttp = 0.01°C

Ptp = 0.6117 kPa

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Thermodynamics



Phase diagramsAlong AB line: rate at which solid sublimes to form a

gas=rate at which gas condenses to form a solid

Along BC line: rate at which liquid boils to form a

gas=rate at which gas condenses to form a liquid

Along BD line: rate at which solid melts to form a

liquid=rate at which liquid freezes to form a solid

The triple point is the temperature and pressure at which

all three phases can exist in equilibrium.

Above the critical point, molecules are unable to liquify.

The heat of fusion is the amount of energy given off

when a substance freezes (or the amount of energy the

substances requires to liquefy).

The heat of vaporization is the amount of energy given

off when a gas liquefies (or the amount of energy needed

to vaporize the liquid).

(Note the difference between the two figures)

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Thermodynamics



Phase diagram of water

Allotropic forms of

solid phases:

Pure substances can

exist in a number of

different solid phases

Pure substances can have multiple ‘triple points’

but there exists only one triple point where all the

three phases can exist together.

The other ‘triple points’ can have two solid phases

and one liquid phase or three solid phases

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Thermodynamics



Regelation

Regelation is the phenomenon

of melting under pressure and

freezing again when the

pressure is reduced.

Regelation occurs only for substances, such as ice,

that have the property of expanding upon freezing,

for the melting points of those substances decrease

with increasing external pressure.

The melting point of ice falls by 0.0072 °C for each

additional atm of pressure applied. For example, a

pressure of 500 atmospheres is needed for ice to

melt at −4 °C.

These two examples, usually cited, as NOT due to regelation

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Thermodynamics



Phase diagram of Carbon-dioxide

The triple-point pressure is greater than

normal atmospheric pressure which is

very unusual.

At one atmosphere, we see CO2 either as

a gas or as a solid.

Therefore, the commonly observed

phase- transition under conditions of

atmospheric pressure of about 100

kPa is a sublimation from solid

directly to vapor, without passing

through a liquid phase, which is why

solid carbon dioxide is commonly

referred to as dry ice.

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Thermodynamics



Supercritical fluids

Supercritical CO2

Supercritical N2

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Thermodynamics



Property tables

• For most substances, the relationships among thermodynamic

properties are too complex to be expressed by simple equations.

• Therefore, properties are frequently presented in the form of tables.

• Some thermodynamic properties can be measured easily, but others

cannot and are calculated by using the relations between them and

measurable properties.

• The results of these measurements and calculations are presented

in tables in a convenient format.

In your text book, Please see Tables A-4 and A-5

Table A-4: Saturation properties of water temperature basis

Table A-5: Saturation properties of water pressure basis

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Thermodynamics



Enthalpy: A new property

It’s a Combination Property

The combination (u + Pv) is

frequently encountered in the

analysis of control volumes.

The product

pressure volume has energy units.

(N/m2 )*(m3)

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Thermodynamics



A quick look at the property tables

Table

A4/A5

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Thermodynamics



Table A-4

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Thermodynamics



Table A-6 and A-7Superheated water vapor

Compressed liquid water

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Thermodynamics



Van der Waals equation of state

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Thermodynamics



Percentage error: Equations of State

For Nitrogen

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Thermodynamics



Percentage error with ideal gas law

For Water

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