# TKP4175 - Thermodynamic Methods

# About

### Examination arrangement

Examination arrangement: Written examination

Grade: Letters

Evaluation form | Weighting | Duration | Examination aids | Grade deviation |
---|---|---|---|---|

Written examination | 100/100 | 4 hours | C |

### Course content

The theory of partial and total differentials, and the chain rule of differentiation. Energy functions, fundamental relations and canonical variables. Equations of state for the fluid state. Unit operations in chemical engineering. Control volume theory applied to kinetic, potential and chemical energies. Thermodynamic equilibrium. Vapor-liquid equilibrium. Multi-component phase equilibrium. Chemical equilibria in ideal gases. Adiabatic combustion temperature. Sources of thermodynamic data with emphasis on the standard state. Heat engines using ideal gas as work fluid. Entropy production. Exergy analysis of stationary processes.

### Learning outcome

At the end of the course the students will:

- Know the early history and chronology of the first and second laws of thermodynamics.

- Understand the current standing and the importance of thermodynamic methods in teaching, industry and research.

- Understand the theoretical differences between thermodynamic state theory and fluid flow and transport processes.

- Apply the phase concept to gases, liquids and solids.

- Be able to initiate and scrutinize and manage thermodynamic development programs in industry or research.

- Use the thirteen (13) most prominent thermodynamic state variables: Internal energy, enthalpy, Gibbs energy, Hemlholtz energy, entropy, volume, mole number, temperature, pressure, chemical potential, heat capacity, expansivity and compressibility on relevant problems.

- Derive the total differential of an arbitrary thermodynamic state function.

- Calculate thermodynamic state and equilibrium conditions departing from a suitable equation of state.

- Transform energy related problems from one energy function to another using Legendre transformations.

- Decide on the Euler homogeneous properties (scaling properties) of thermodynamic state variables.

- Derive the total differential of an arbitrary thermodynamic function with arbitrary free variables.

- Derive mass and energy balances for closed and open control volumes having one or several chemical components.

- Derive and linearize invertible equation systems for the solution of homogeneous reaction and/or phase equilibria using Gibbs and Helmholtz energy minimization.

- Derive all seven (7) Legendre trransformations of internal energy.

- Calculate the internal energy, enthalpy, entropy, heat capacity and chemical potential of ideal gasses at a given temperature, pressure (or volume), and composition using common tables for the standard states and simple temperature functions for the ideal gas heat capacity of each component.

- Calculate chemical equilibrium for one (1) chemical reaction in ideal gas phase at given temperature, pressure (or volume), and composition.

- Calculate independent reactions in a multicomponent mixture using matrix methods.

- Calculate state changes for simple process units like for example: valves, compressors, mixers and heat exchangers using ideal gass, second virial equation, or the van der Waals equation.

- Calculate the thermodynamic efficiency of Stirling, Ericsson, Brayton, Carnot, Otto and Rankine machines using ideal gas as the work fluid.

- Calculate the exergy efficiency of a stationary process.

### Learning methods and activities

The course is given as a combination of class-room lectures and practical calculations in the auditorium. Compulsory in-depth exercises are supervised by the student assistents. Some of the exercises require programming skills - in particular the parts that cover chemical reaction equilibria and phase equilibria.

### Compulsory assignments

- Exercises

### Further on evaluation

If there is a re-sit examination, the examination form may be changed from written to oral.

### Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

### Recommended previous knowledge

Prior experience with programming in Python, Ruby, or Matlab is very useful.

Physical chemistry and elementary thermodynamics, chemical process technology, kinetic gas theory, differential calculus, and abstract linear algebra at the undergraduate university level.

### Course materials

T. Haug-Warberg, Den termodynamiske arbeidsboken, Kolofon forlag (2005), english version is available.

# Timetable

Detailed timetable# Examination

Examination arrangement: Written examination

Term | Statuskode | Evaluation form | Weighting | Examination aids | Date | Time | Room * |
---|---|---|---|---|---|---|---|

Spring | ORD | Written examination | 100/100 | C |

- * The location (room) for a written examination is published 3 days before examination date.