Advanced Thermodynamics: Lecture 1 Shivasubramanian Gopalakrishnan - - PowerPoint PPT Presentation

Advanced Thermodynamics: Lecture 1

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

ME 661 : Advanced Thermodynamics

Location : CDEEP A1 A2 Timings : Slot 13 : MoTh 1830 – 2000 Office 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.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Topics covered

Concepts of classical thermodynamics. Application of I and II laws to closed and open systems. Availability analysis of thermal systems and the concept of energy conservation. Phase and reaction equilibria. Equilibrium constants. calculation of equilibrium composition of multi component gaseous mixtures. Equations of state and calculation of thermodynamics and transport properties of substances. Kinetic Theory of gases. Brief review of probability and

• statistics. Statistical Thermodynamics, Boltzmann,

Fermi-dirac and Bose Einstein Statistics,Fluctuations,Monoatomic and Diatomic Gases, introduction to Classical StatisticalMechanics, phase space, liouville equation,

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Classical Thermodynamics

Therme – Greek for heat Dynamis – Greek for power A branch of science which takes a Macroscopic view of

• systems. Assume Continuum.

Deals with transfer / conversion of energy from one form to another. Fundamentals are entirely empirical. Based on 4 simple laws and simple mathematics.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

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 !!

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

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 and surroundings. The choice of the system and boundary is very important in defining and solving any problem.

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Types of systems

Open system ⇒ Allows for mass and energy transfer between system and surroundings. Closed system ⇒ Allows only energy transfer between system and surroundings. No mass transfer is allowed. Isolated system ⇒ No mass or energy transfer allowed between the system and surroundings.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Properties of a system

Any characteristic of a system is called a property. Properties can either be intensive or extensive. Intensive properties: are those which are independent of mass of a system. Examples: Temperature, density, pressure etc Extensive properties: that which depend on the size or the mass of the system. Examples: Total mass, Total momentum, Volume etc.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Thermodynamics deals with equilibrium states. The word equilibrium implies a state of balance. In an equilibrium state there are no unbalanced potentials (or driving forces) within the system. A system in equilibrium experiences no changes when it is isolated from its surroundings. Thermal equilibrium – if temperature is uniform throughout the system. Mechanical equilibrium - no change in pressure with time.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Thermodynamics deals with equilibrium states. The word equilibrium implies a state of balance. In an equilibrium state there are no unbalanced potentials (or driving forces) within the system. A system in equilibrium experiences no changes when it is isolated from its surroundings. Thermal equilibrium – if temperature is uniform throughout the system. Mechanical equilibrium - no change in pressure with time. Chemical equilibrium - if chemical composition is constant. State Postulate: The state of a simple compressible system is completely defined by two independent, intensive properties.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Any change that a system undergoes from one equilibrium state to another is called a process, and the series of states through which a system passes during a process is called the path of the process. When a process proceeds in such a manner that the system remains 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 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

The prefix iso- is often used to designate a process for which a particular 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 to its initial state at the end of the process. That is, for a cycle the initial and final states are identical.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Zeroth Law of thermodynamics

States that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. By replacing the third body with a thermometer, the zeroth law can 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 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Temperature scales provide us with a common standardized basis for temperature measurement. Needs 2 reference points and an interpolation method. Celsius scale. also known as centigrade scale. reference points 0oC – melting point of ice. 100oC – boiling point of

• water. Anything missing???

Farhenheit scale . reference points 32oF – melting point of

• ice. 96oF – blood-warm.

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

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Properties of pure substances

A substance that has a fixed chemical composition throughout is called a pure substance. Water, nitrogen, helium, and carbon dioxide, for example, are all pure substances. A mixture of two or more phases of a pure substance is still a pure substance as long as the chemical composition of all phases is the same A mixture of ice and water – pure substance

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Properties of pure substances

A substance that has a fixed chemical composition throughout is called a pure substance. Water, nitrogen, helium, and carbon dioxide, for example, are all pure substances. A mixture of two or more phases of a pure substance is still a pure substance as long as the chemical composition of all phases is the same A mixture of ice and water – pure substance A mixture of liquid air and gaseous air – not a pure substance

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Constant pressure phase change

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Subcooled liquid: compressed liquid that is not about to vaporize. 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 a saturated liquid–vapor mixture since the liquid and vapor phases coexist in equilibrium at these states. Superheated vapor: Vapor which is not about condense.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

The amount of energy absorbed or released during a phase-change process is called the latent heat. The amount of energy absorbed during melting is called the latent heat of fusion and is equivalent to the amount of energy released during freezing. Energy absorbed during vaporization is called the latent heat

• f vaporization and is equivalent to the energy released during

condensation.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

T-v diagram

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

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

T-v diagram of a pure substance

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

P-v diagram of a pure substance

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

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

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

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

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

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

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

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

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Equation of state

Any equation that relates the pressure, temperature, and specific volume of a substance is called an equation of state. In 1662, Robert Boyle, an Englishman, observed during his experiments with a vacuum chamber that the pressure of gases is inversely proportional to their volume. In 1802, J. Charles and J. Gay-Lussac, Frenchmen, experimentally determined that at low pressures the volume of a gas is proportional to its temperature. P = R T ν where the constant of proportionality R is called the gas constant. Equation is called the ideal-gas equation of state

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

The gas constant R is different for each gas is determined from R = Ru M where Ru is the universal gas constant and M is the molar mass of the gas. The molar mass M can simply be defined as the mass of one mole (also called a gram-mole, abbreviated gmol) of a substance in grams, or the mass of one kmol (also called a kilogram-mole, abbreviated kgmol) in kilograms.

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

The gas constant R is different for each gas is determined from R = Ru M where Ru is the universal gas constant and M is the molar mass of the gas. The molar mass M can simply be defined as the mass of one mole (also called a gram-mole, abbreviated gmol) of a substance in grams, or the mass of one kmol (also called a kilogram-mole, abbreviated kgmol) in kilograms. The constant Ru is the same for all substances, and its value is Ru = 8.31447kJ/kmol · K

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Gases deviate from ideal-gas behavior significantly at states near the saturation region and the critical point. This deviation from ideal-gas behavior at a given temperature and pressure can be corrected by introducing a correction factor called the compressibility factor Z defined as Z = Pν RT The behavior of different gases is different at varying pressures and

• temperatures. Though if the pressure and temperature are

normalize with respective critical points, then at these reduced pressure and temperatures, the behavior of gases are quite similar. PR = P Pcrit TR = T Tcrit

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Compressibility factor for various gases

Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661

Other equations of state

Van der Waal’s equation of state ⇣ P + a v2 ⌘ (ν − b) = RT Where, a = 27R2T 2

crit

64Pcrit and b = RTcrit 8Pcrit Beattie-Bridgeman EOS P = RuT ¯ ν2 ⇣ 1 − c ¯ νT 3 ⌘ (¯ ν + B) − A ¯ ν2 Where, A = A0 ⇣ 1 − a ¯ ν ⌘ and B = B0 ✓ 1 − b ¯ ν ◆

Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661