# TKP4175 - Thermodynamic Methods

### Examination arrangement

Examination arrangement: Home examination

Evaluation form Weighting Duration Examination aids Grade deviation
Home examination 100/100 A

### 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. Multicomponent 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:

Master thermodynamic analyses of physico-chemical equilibrium problems linked to the mathematical modeling of chemical multicomponent systems and numerical calculation of chemical and phase equilibrium in said systems.

Implement at least one thermodynamic equation of state or activity coefficient model in so-called canonical variables of the model. The implementation must be verified (unit tested) and shall contain symbolic derivatives of first and second order in the natural (canonical) variables of the model. The model will be used to calculate a complete phase diagram in the coordinates specified by the teacher.

Understand what make canonical variables different from other (more arbitrary) variables, understand what makes an equation of state different from an activity coefficient model, understand how to apply the criteria of thermodynamic equilibrium to multicomponent mixtures, understand what are the necessary and sufficient conditions for optimality of thermodynamic potentials, and understand the significance of Gibbs-Duhem's equation applied to multicomponent system for verifying thermodynamic consistency of computational results.

Apply partial differentiation of functions with many variables, perform differential calculus of said state functions, make iterative solutions of nonlinear equations systems, do unit testing of computer code, and verify thermodynamic calculation results.

Derive thermodynamic state information for liquids and gasses from a suitable potential (typically Gibbs or Helmholtz energy), implement the selected potential with first and second order derivatives into a suitable programming language, and apply the computer code to solve thermodynamic equilibrium problems related to chemical reaction and phase equilibria using Newton's method of iteration.

### Learning methods and activities

Classroom lectures (3 hours per week), tutored programming (2 hours per week), Individual programming (4-8 hours per week) and report writing (4 hours per week). The students can collaborate in groups of 2-3 people if they so wish. Lectures and exercises are mandatory and can be used to bring over information that is not necessarily written anywhere. Experience based knowledge for example.

### Compulsory assignments

• Partial submission

### Further on evaluation

Home exam: The student is asked to explain the theory for disseminating and solving the problem assigned by the teacher, explain details concerning the implementation, perform unit testing of the computer code, and summarise all of it including relevant calculation results in an essay of length and depth equivalent to 2-3 chapters in a MSc thesis. The nominal length of the report is 28 A4 pages printet in 11 point font and with 25 mm margins. This means approximately two pages of written text per week during the semester. The report shall as a minimum contain at least one page of figures of good quality and a maximum of three pages of such illustrations. The figure captions and the axes labels shall use 10 pt font. The figures should keep a high standard and must be positioned adequately in the report. The captions are made self-explanatory without undue references to the main text. The report should preferably be given an individual touch and feel. The same applies to the equations and to the program code. Copying from external sources is not allowed.

The academic, linguistic and aesthetic profiles of the report are weighted 50%, 25% and 25%, respectively. The best of the reports will graded on the scale A-F. The other reports will be given a grade relative to this. The best grade will not necessarily be an A and the grades will not necessarily follow a Gaussian distribution. If the student fails to deliver a satisfactory report, or want to improve her grade, the entire course must be re-taken.

### 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.

### Required previous knowledge

TKP4107 Chemical Engineering Thermodynamics, TMA4100 Mathematics 1 (differential calculus, Newton's iteration method), TMA4105 Mathematics 2 (multivariable function analysis), TMA4115 Mathematics 3 (linear algebra), TDT4102 Procedure and object oriented programming, or courses equivalent to these.

### Course materials

T. Haug-Warberg, Den termodynamiske arbeidsboken, Kolofon forlag (2005), English version is available. A detailed curriculum list will be given at the startup.

More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Intermediate course, level II

Coursework

Term no.: 1
Teaching semester:  SPRING 2021

No.of lecture hours: 4
Lab hours: 2
No.of specialization hours: 6

Language of instruction: English

Location: Trondheim

Subject area(s)
• Technological subjects
Contact information
Course coordinator:

Department of Chemical Engineering

Phone:

# Examination

#### Examination arrangement: Home examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam
Spring ORD Home examination 100/100 A
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

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