MME 311: Metallurgical Thermodynamics Notes

Metallurgical Thermodynamics vs. General Thermodynamics

• Metallurgical thermodynamics is a specialized branch of general thermodynamics, focusing on the application of thermodynamic principles to metals and alloys.

• General Thermodynamics:

  • Deals with the relationships between heat, work, and energy.

  • Provides a broad understanding of thermodynamic principles, including the laws of thermodynamics and system equilibrium.

  • Applicable to all fields of science and engineering.

• Metallurgical Thermodynamics:

  • Focuses on the production, processing, and properties of metals and alloys.

  • Deals with the thermodynamic aspects of metallurgical processes like melting, casting, refining, and alloying.

  • Concerned with the behavior of metals and alloys under high temperatures, pressures, and chemical environments.

• Key Differences:

  1. Focus:

     • General thermodynamics: Fundamental principles.

     • Metallurgical thermodynamics: Application to metallurgy.

  2. Application:

     • General thermodynamics: Broad range of applications.

     • Metallurgical thermodynamics: Production and processing of metals and alloys.

  3. Systems:

     • General thermodynamics: Gases, liquids, and solids.

     • Metallurgical thermodynamics: Metals and alloys (complex systems).

  4. Temperature and Pressure Ranges:

     • Metallurgical thermodynamics often involves high temperatures (e.g., above 1000°C) and pressures not typical in general thermodynamics.

  5. Chemical Reactions:

     • Metallurgical thermodynamics involves complex chemical reactions like oxidation, reduction, and alloying, not typically considered in general thermodynamics.

Popular Textbooks on Metallurgical Thermodynamics

1. "Metallurgical Thermodynamics" by O. Kubaschewski and C. B. Alcock: A classic comprehensive introduction.

2. "Thermodynamics of Materials" by David R. Gaskell: Covers thermodynamic principles underlying various materials processes, including metallurgical ones.

3. "Metallurgical Thermodynamics: Principles and Applications" by G. K. Sigworth: Detailed introduction covering phase equilibria, solution thermodynamics, and electrochemistry.

4. "Thermodynamics in Materials Science" by Robert T. DeHoff: Application of thermodynamic principles to materials science, including metallurgy, ceramics, and polymers.

5. "Metallurgical and Materials Thermodynamics" by Y. Austin Chang and J. P. Neumann: Comprehensive introduction to the thermodynamics of alloys, phase equilibria, and materials processing.

6. "Principles of Metallurgical Thermodynamics" by A. K. Biswas: Detailed introduction to the principles of metallurgical thermodynamics, including phase equilibria, solution thermodynamics, and electrochemistry.

7. "Thermodynamics of Metallurgical Processes" by J. M. Toguri: Covers thermodynamic principles underlying various metallurgical processes, including smelting, refining, and alloying.

Example 1: Gibbs Free Energy Calculation for Steel Alloy

• Problem: Calculate the Gibbs free energy of formation of a steel alloy with composition Fe-0.5C-0.2Mn-0.1Si (in weight percent).

• Given Thermodynamic Data:

  • $AG°Fe = -10.5 \, \text{kJ/mol}$

  • $AG°C = 0 \, \text{kJ/mol}$

  • $AG°Mn = -15.1 \, \text{kJ/mol}$

  • $AG°Si = -20.6 \, \text{kJ/mol}$

  • Interaction Parameters:

    • $ΩFe-C = -20.0 \, \text{kJ/mol}$

    • $ΩFe-Mn = -10.0 \, \text{kJ/mol}$

    • $ΩFe-Si = -15.0 \, \text{kJ/mol}$

    • $ΩC-Mn = 5.0 \, \text{kJ/mol}$

    • $ΩC-Si = 10.0 \, \text{kJ/mol}$

    • $ΩMn-Si = 0 \, \text{kJ/mol}$

• Equation:

  • $ΔG = xFeΔG°Fe + xCΔG°C + xMnΔG°Mn + xSiΔG°Si + RT[xFe \ln xFe + xC \ln xC + xMn \ln xMn + xSi \ln xSi] + ΩFe-CxFe xC + ΩFe-Mn xFe xMn + ΩFe-Si xFe xSi + ΩC-Mn xC xMn + ΩC-Si xC xSi + ΩMn-Si xMn xSi$

• Calculations:

  1. Mole Fractions:

     • $xFe = 99.2/100 = 0.992$

     • $xC = 0.5/100 = 0.005$

     • $xMn = 0.2/100 = 0.002$

     • $xSi = 0.1/100 = 0.001$

  2. Natural Logarithms:

     • $\ln xFe = \ln 0.95 = -0.0513$

     • $\ln xC = \ln 0.005 = -4.6052$

     • $\ln xMn = \ln 0.002 = -5.9957$

     • $\ln xSi = \ln 0.001 = -6.9078$

  3. Plugging in values:

     • $ΔG = (0.95)(-10.5) + (0.005)(0) + (0.002)(-15.1) + (0.001)(-20.6) + (8.314/1000)(298)[(0.95)(-0.0513) + (0.005)(-4.6052) + (0.002)(-5.9957) + (0.001)(-6.9078)] + (-20.0)(0.005) + (-10.0)(0.002) + (-15.0)(0.001) + (5.0)(0.002) + (10.0)(0.001) + (0)(0.001)$

     • $ΔG = -9.975 + 0 - 0.0302 - 0.0206 + (2.478)[-0.0487 - 0.0230 - 0.0120 - 0.0069] - 0.1 - 0.02 - 0.015 + 0.01 + 0.01 + 0$

     • $ΔG = -9.975 - 0.0302 - 0.0206 - 0.226 - 0.1 - 0.02 - 0.015 + 0.02$

     • $ΔG ≈ -10.3 \, \text{kJ/mol}$

• Derivation of the Equation:

  • The equation is derived from: $ΔG = ΔH - TΔS$

  • Where, $ΔH = xFeΔH°Fe + xCΔH°C + xMnΔH°Mn + xSiΔH°Si + ΩFe-CxFe xC + ΩFe-Mn xFe xMn + ΩFe-Si xFe xSi + ΩC-Mn xC xMn + ΩC-Si xC xSi$

First Law of Thermodynamics

• Statement: Energy cannot be created or destroyed, only converted from one form to another.

• Mathematical Expression:

  • $ΔE = Q - W$

    • Where:

      • $ΔE$ is the change in energy of the system.

      • $Q$ is the heat added to the system.

      • $W$ is the work done by the system.

• Key Concepts:

  1. Energy: The ability to do work or cause change.

  2. System: A region or collection of matter being studied.

  3. Isolated System: A system that does not exchange energy or matter with its surroundings.

  4. Heat: The transfer of energy due to a temperature difference.

  5. Work: The transfer of energy through a force applied over a distance.

• Implications:

  1. Energy Conservation: The total energy of an isolated system remains constant.

  2. Energy Conversion: Energy can be converted from one form to another, but the total remains constant.

  3. No Perpetual Motion: It's impossible to create energy from nothing or convert all energy into useful work.

• Examples:

  1. Car engine: Chemical energy (gasoline) → Mechanical energy (propulsion).

  2. Power plant: Thermal energy (coal) → Electrical energy.

  3. Refrigerator: Electrical energy → Thermal energy (cooling).

Heat and Internal Energy

• Heat (Q):

  • The transfer of energy due to a temperature difference.

  • Energy transferred from a higher temperature system to a lower temperature system.

  • A path-dependent function.

• Internal Energy (U):

  • The total energy of a system.

  • Includes kinetic energy, potential energy, vibrational energy, and rotational energy of particles.

  • Measure of energy stored within the system.

• Relationship:

  • Changing internal energy: Adding/removing heat.

  • First Law of Thermodynamics: $ΔU = Q - W$

• Types of Internal Energy:

  1. Kinetic Energy: Motion of particles.

  2. Potential Energy: Position of particles.

  3. Vibrational Energy: Vibrations of particles.

  4. Rotational Energy: Rotation of particles.

  5. Electronic Energy: Energy of electrons.

• Units:

  • Joules (J) or calories (cal).

  • $1 \, \text{J} = 0.239 \, \text{cal}$

• Examples:

  1. Hot coffee vs. cold coffee: Hot coffee has higher internal energy due to faster particle motion.

  2. Car engine burning gasoline: Internal energy of gasoline converted to kinetic energy.

  3. Refrigerator: Removes heat, decreasing internal energy.

Work

• Definition: Transfer of energy through a force applied over a distance.

• Equation:

  • $W = F × d$

    • Where:

      • $W$ is work.

      • $F$ is force.

      • $d$ is distance.

• Units:

  • Joules (J) or foot-pounds (ft-lb).

  • $1 \, \text{J} = 0.7376 \, \text{ft-lb}$

• Types of Work:

  1. Mechanical Work: Force causing movement.

  2. Thermal Work: Energy transfer through heat.

  3. Electrical Work: Energy transfer through electric current.

  4. Chemical Work: Energy transfer through chemical reaction.

• Examples:

  1. Lifting a weight: Force applied over a distance.

  2. Car engine: Force applied to wheels.

  3. Refrigerator: Force applied to air molecules.

  4. Bicycle: Force applied to pedals.

• Work and Energy:

  • Work is a way of transferring energy.

  • Work done on an object increases its energy; work done by an object decreases its energy.

• Conservation of Energy:

  • Energy cannot be created or destroyed, only converted.

• Efficiency:

  • Measure of work done compared to energy input.

  • $\text{Efficiency} = (\frac{\text{Work output}}{\text{Energy input}}) × 100\%$

  • Example: Car engine converting 20% of gasoline energy into mechanical work has 20% efficiency.

Reversible and Irreversible Processes

• Reversible Process:

  • Can be reversed without any change in the surroundings; the system returns to its initial state.

  • System and surroundings in equilibrium at all times.

• Characteristics:

  1. Slow and gradual: System and surroundings remain in equilibrium.

  2. System and surroundings in equilibrium: Temperature, pressure, etc., are equal.

  3. Can be reversed: By reversing the external forces or conditions.

  4. No entropy change.

• Examples:

  1. Isothermal expansion of a gas: Can be compressed back to its original state.

  2. Adiabatic compression of a gas: Can be expanded back to its original state.

  3. Carnot cycle: Consists of four reversible processes.

• Irreversible Process:

  • Cannot be reversed without any change in the surroundings; the system cannot return to its initial state.

  • System and surroundings are not in equilibrium.

• Characteristics:

  1. Fast and spontaneous.

  2. System and surroundings not in equilibrium.

  3. Cannot be reversed.

  4. Entropy change: Increases disorder.

• Examples:

  1. Heat transfer: From hotter to cooler body.

  2. Friction: Energy lost as heat cannot be recovered.

  3. Chemical reactions: Reactants cannot be converted back without external influence.

Adiabatic and Isothermal Processes

• Adiabatic Process:

  • No heat transfer between the system and surroundings.

  • Thermally isolated system.

• Characteristics:

  1. No heat transfer.

  2. Temperature change.

  3. Work done.

  4. Entropy change.

• Examples:

  1. Expansion of a gas (rapid).

  2. Compression of a gas (rapid).

  3. Shock waves.

• Isothermal Process:

  • Temperature of the system remains constant.

  • Thermal equilibrium with surroundings.

• Characteristics:

  1. Constant temperature.

  2. Heat transfer.

  3. Work done.

  4. Entropy change.

• Examples:

  1. Phase changes (melting, boiling).

  2. Chemical reactions (some).

  3. Heat transfer (between systems at the same temperature).

• Comparison:

  • Adiabatic: No heat transfer, temperature varies.

  • Isothermal: Heat transfer allowed, temperature constant.

Endothermic and Exothermic Reactions

• Endothermic Reaction:

  • Absorbs heat from the surroundings.

  • Requires energy.

• Characteristics:

  1. Heat absorption.

  2. Temperature decrease in surroundings.

  3. Positive enthalpy change ($ΔH$).

• Examples:

  1. Photosynthesis.

  2. Melting of ice.

  3. Evaporation of water.

• Exothermic Reaction:

  • Releases heat to the surroundings.

  • Releases energy.

• Characteristics:

  1. Heat release.

  2. Temperature increase in surroundings.

  3. Negative enthalpy change ($ΔH$).

• Examples:

  1. Combustion of gasoline.

  2. Burning of wood.

  3. Respiration.

• Comparison:

  • Endothermic: Absorbs heat, temperature decreases, $ΔH$ is positive.

  • Exothermic: Releases heat, temperature increases, $ΔH$ is negative.

Henry's Law

• Statement: The amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid.

• Mathematical Expression:

  • $C = kP$

    • Where:

      • $C$ is the concentration of the gas in the liquid.

      • $k$ is Henry's Law constant.

      • $P$ is the partial pressure of the gas above the liquid.

• Physical Meaning:

  • Increase in partial pressure increases the amount of gas dissolved; decrease in partial pressure decreases the amount of gas dissolved.

• Examples:

  1. Carbonated beverages: CO2 dissolved under pressure releases when pressure is removed.

  2. Scuba diving: Nitrogen dissolves in the bloodstream under pressure.

  3. Medical applications: Anesthesia gases dissolved in the bloodstream.

• Assumptions:

  1. Gas is ideal.

  2. Liquid is a solvent.

  3. Constant temperature and pressure.

  4. No reaction between gas and liquid.

• Limitations:

  1. Non-ideal gases.

  2. High pressures.

  3. Complex systems.

• Applications:

  1. Gas solubility prediction.

  2. Gas separation.

  3. Medical applications.

Kirchhoff's Law

• Statement: The heat transferred to a system is equal to the heat transferred out of the system; the temperature of the system remains constant.

• Mathematical Expression:

  • $Qin = Qout$

• Temperature and Heat Transfer:

  • $ΔT = \frac{Q}{C}$

    • Where:

      • $ΔT$ is the change in temperature.

      • $Q$ is the heat transferred.

      • $C$ is the heat capacity.

• Assumptions:

  1. Thermal equilibrium.

  2. Closed system.

  3. Steady-state system.

• Limitations:

  1. Non-equilibrium systems.

  2. Time-dependent systems.

  3. Non-linear systems.

• Applications:

  1. Heat transfer calculations.

  2. Temperature calculations.

  3. Thermal design.

• Examples:

  1. Heat exchanger.

  2. Insulation.

  3. Refrigeration cycle.