Advanced Thermodynamics: Lecture 1

Advanced Thermodynamics: Lecture 1

Shivasubramanian [email protected]

Shivasubramanian Gopalakrishnan [email protected] ME 661

ME 661 : Advanced Thermodynamics

Location : CDEEP A1 A2

Timings : Slot 13 : MoTh 1830 – 2000

O�ce hours : Strictly by appointment only. No walk ins!

3 Midsems, 1 Final

Midsem 1: 17th August 1830 – 2030 (2 hours)

Midsem 2: Midesem week as per Institute timetable

Midsem 3: 12th October 1830 – 2030 (2 hours)

Grade weightage: 20% each Midsem and 40 % Final

Grading will be on a curve.

Lectures will be available on Moodle.


Topics covered

Concepts of classical thermodynamics. Application of I and IIlaws to closed and open systems. Availability analysis ofthermal systems and the concept of energy conservation.Phase and reaction equilibria. Equilibrium constants.calculation of equilibrium composition of multi componentgaseous mixtures. Equations of state and calculation ofthermodynamics and transport properties of substances.

Kinetic Theory of gases. Brief review of probability andstatistics. Statistical Thermodynamics, Boltzmann,Fermi-dirac and Bose EinsteinStatistics,Fluctuations,Monoatomic and Diatomic Gases,introduction to Classical StatisticalMechanics, phase space,liouville equation,


Classical Thermodynamics

Therme – Greek for heat

Dynamis – Greek for power

A branch of science which takes a Macroscopic view ofsystems. Assume Continuum.

Deals with transfer / conversion of energy from one form toanother.

Fundamentals are entirely empirical.

Based on 4 simple laws and simple mathematics.


4 Laws of Thermodynamics

Zeroth Law ) Defines temperature

First Law ) Defines energy

Second Law ) Defines Entropy

Third Law ) Gives numerical value to entropy

All laws are universally valid and cannot be violated !!


Some Definitiions

System : The part of the universe which we choose to study.

Surroundings : The rest of the universe.

Boundary : The interface between the system andsurroundings.

The choice of the system and boundary is very important indefining and solving any problem.Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition


Types of systems

Open system ) Allows for mass and energy transfer betweensystem and surroundings.

Closed system ) Allows only energy transfer between systemand surroundings. No mass transfer is allowed.

Isolated system ) No mass or energy transfer allowedbetween the system and surroundings.


Properties of a system

Any characteristic of a system is called a property. Properties caneither be intensive or extensive.

Intensive properties: are those which are independent ofmass of a system. Examples: Temperature, density, pressureetc

Extensive properties: that which depend on the size or themass of the system. Examples: Total mass, Total momentum,Volume etc.


Thermodynamics deals with equilibrium states. The wordequilibrium implies a state of balance. In an equilibrium state thereare no unbalanced potentials (or driving forces) within the system.A system in equilibrium experiences no changes when it is isolatedfrom its surroundings.

Thermal equilibrium – if temperature is uniform throughoutthe system.

Mechanical equilibrium - no change in pressure with time.

Chemical equilibrium - if chemical composition is constant.

State Postulate: The state of a simple compressible systemis completely defined by two independent, intensive properties.


Any change that a system undergoes from one equilibrium state toanother is called a process, and the series of states through whicha system passes during a process is called the path of the process.

When a process proceeds in such a manner that the systemremains infinitesimally close to an equilibrium state at all times, it

is called a quasi- static, or quasi-equilibrium, process.Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition


The prefix iso- is often used to designate a process for which aparticular property remains constant.

Isothermal process – temperature is constant.

Isobaric process – pressure is constant.

Isochoric or Isometric process – specific volume is constant.

Isenthalpic process – specific enthalpy is constant.

Isentropic process – entropy is constant.

Cycle: A system is said to have undergone a cycle if it returns toits initial state at the end of the process. That is, for a cycle theinitial and final states are identical.


Zeroth Law of thermodynamics

States that if two bodies are in thermal equilibrium with a thirdbody, they are also in thermal equilibrium with each other.

By replacing the third body with a thermometer, the zeroth lawcan be restated as two bodies are in thermal equilibrium if both

have the same temperature reading even if they are not in contact.Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition


Temperature scales provide us with a common standardized basisfor temperature measurement. Needs 2 reference points and aninterpolation method.

Celsius scale. also known as centigrade scale. referencepoints 0oC – melting point of ice. 100oC – boiling point ofwater. Anything missing???

Farhenheit scale . reference points 32oF – melting point ofice. 96oF – blood-warm.

Kelvin scale. absolute, thermodynamic temperature scale.Null point is absolute zero.


Properties of pure substances

A substance that has a fixed chemical composition throughout iscalled a pure substance. Water, nitrogen, helium, and carbondioxide, for example, are all pure substances.

A mixture of two or more phases of a pure substance is still a puresubstance as long as the chemical composition of all phases is thesame

A mixture of ice and water – pure substance

A mixture of liquid air and gaseous air – not a pure substance


Constant pressure phase change

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition


Subcooled liquid: compressed liquid that is not about tovaporize.

Saturated liquid: Liquid that is about to vaporize.

Saturated vapor: Vapor that is about to condense.

A substance at states between 2 and 4 is referred to as asaturated liquid–vapor mixture since the liquid and vaporphases coexist in equilibrium at these states.

Superheated vapor: Vapor which is not about condense.


The amount of energy absorbed or released during aphase-change process is called the latent heat.

The amount of energy absorbed during melting is called thelatent heat of fusion and is equivalent to the amount ofenergy released during freezing.

Energy absorbed during vaporization is called the latent heatof vaporization and is equivalent to the energy released duringcondensation.


T-v diagram

The critical point is defined as the point at which the saturatedliquid and saturated vapor states are identical.



T-v diagram of a pure substance



P-v diagram of a pure substance



P-v diagram of a pure substance which contracts on freezing



P-v diagram of a pure substance which expands on freezing



P-v -t surface of a pure substance which contracts on freezing



P-v -t surface of a pure substance which expands on freezing



Equation of state

Any equation that relates the pressure, temperature, andspecific volume of a substance is called an equation of state.

In 1662, Robert Boyle, an Englishman, observed during hisexperiments with a vacuum chamber that the pressure ofgases is inversely proportional to their volume.

In 1802, J. Charles and J. Gay-Lussac, Frenchmen,experimentally determined that at low pressures the volume ofa gas is proportional to its temperature.

P = R

T

⌫

where the constant of proportionality R is called the gas constant.Equation is called the ideal-gas equation of state


The gas constant R is di↵erent for each gas is determinedfrom

R =R

u

M

where R

u

is the universal gas constant and M is the molarmass of the gas.

The molar mass M can simply be defined as the mass of onemole (also called a gram-mole, abbreviated gmol) of asubstance in grams, or the mass of one kmol (also called akilogram-mole, abbreviated kgmol) in kilograms.

The constant Ru is the same for all substances, and its value is

R

u

= 8.31447kJ/kmol · K


Gases deviate from ideal-gas behavior significantly at states nearthe saturation region and the critical point. This deviation fromideal-gas behavior at a given temperature and pressure can becorrected by introducing a correction factor called thecompressibility factor Z defined as

Z =P⌫

RT

The behavior of di↵erent gases is di↵erent at varying pressures andtemperatures. Though if the pressure and temperature arenormalize with respective critical points, then at these reducedpressure and temperatures, the behavior of gases are quite similar.

P

R

=P

P

crit

T

R

=T

T

crit


Compressibility factor for various gases



Other equations of state

Van der Waal’s equation of state

⇣P +

a

v

2

⌘(⌫ � b) = RT

Where,

a =27R2

T

2

crit

64Pcrit

and b =RT

crit

8Pcrit

Beattie-Bridgeman EOS

P =R

u

T

⌫̄2

⇣1� c

⌫̄T 3

⌘(⌫̄ + B)� A

⌫̄2

Where,

A = A

0

⇣1� a

⌫̄

⌘and B = B

0

✓1� b

⌫̄

◆


Advanced Thermodynamics: Lecture 1

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