Thermodynamics Problems

If you are taking a course in basic or advanced physics, one of the tough courses to tackle is thermodynamics. Problems related to this subject can be intimidating for most students at the start.

Thermodynamics is one of the prime branches of physics, which deals with energy changes of all kinds and the interconversion between different forms of energy. It particularly deals with the conversion of heat and energy into useful work. This branch of physics is the forerunner of statistical mechanics and deals with the bulk or macroscopic parameters of the system like temperature, volume and pressure. It is an interdisciplinary subject and it spreads over various other branches of science and engineering.

How to Solve Thermodynamics Problems?
Learning is a process and problem solving is where your understanding of the subject is thoroughly tested. The joy of having solved a problem on your own is incomparable. Not only does it give you confidence, it increases your depth of understanding of the subject. Knowledge of the subject, its concepts and the precise application of that knowledge is really the key to solving any of the problems. Let us see how to go about solving thermodynamic problems.

Know the Thermodynamic Laws and Equations
A good practice before beginning problem solving in any analytical science subject, is to list the basic laws that form the core of that subject, along with other important relations and formulas. In case of thermodynamics problems, you need to understand and note down the basic four laws of thermodynamics and the various relations that are consequences of those laws. In fact it is a good idea to make a comprehensive physics formulas list that you can use anytime.

Most important thermodynamic equations are the expressions for the various thermodynamic potentials. These include all the relations between internal energy, Helmholtz free energy, enthalpy, Gibbs free energy and the less known Landau or grand potential that is taught in advanced thermodynamics courses and the macroscopic thermodynamic variables is necessary. A knowledge of relations between these various potentials is also essential. I suggest that you make a list or table of the most important thermodynamic relations which you can keep in handy while solving problems. Understanding of theory and concepts like thermodynamic equilibrium is absolutely vital.

Understand Basic Calculus, Probability and Statistics
A knowledge of basic integration and differentiation techniques, elementary probability and statistics is necessary to solve problems in thermodynamics. When it comes to any kind of science, knowledge of basic mathematics is inevitable. Probability and statistics knowledge is very useful while solving problems of statistical thermodynamics. Make a list of the important mathematical formulas that you require for solving most thermodynamic problems. You can take guidance from your instructor regarding the mathematical techniques needed.

Know the Nature of the Problem
I cannot tell you how to solve a particular thermodynamic problem, as there are many types. However, there are two types of problems in general. One broad class of problems are of the 'plug-in' type. To get a solution, all you have to do is plug in the values of known quantities into a related thermodynamic relation to get an answer. Another broad class of problems is the analytical type of problems. These require you to work on the given clues and set up an equation for solution. They may require you to manipulate and solve the equations. Some are just teasers (which are generally the multiple choice questions) meant to test your understanding of the subject. Know the nature of the problem and proceed accordingly.

Identify the Known Quantities and Unknowns
One way which can aid you in simplifying the problem is stripping it down to the bare bones. Write down all the values of known variable supplied in the problem and write them clearly. Then identify what exactly you are supposed to find in the problem. In short, list the known and the unknowns. That will help you in seeing the solution more clearly. Sometimes there may be more than one unknowns. See that all the quantities are converted into a uniform system of units before you proceed. This will ensure that you have a solution in the right units.

Write Down Related Thermodynamic Relations
Based on the information provided, look for the thermodynamic relation that provides a relation between the unknown quantities and the known quantities. This is where your thermodynamic relations table will be useful. When there are more than one unknown quantities, you will have to use more than one relations and derive a few quantities before you can piece together the solution.

Set up the Equation and Calculate
Last part, of course, is to sit and calculate by solving the equation you have set up for solution of the unknown quantity. Write every step of calculation cleanly and try to simplify it, as much as possible, at every step. If you have gone by the right route, a solution will not elude you. If you do go wrong and your answers don't tally, with the right ones, then you have to go back and check where you went wrong. Keep at it till the right solution is found!

There is no substitute to persistence and thinking on your own, when it comes to problems solving of any kind. There is no easy way out.