How to Solve Thermodynamics Problems?

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.

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 problem.

A good practice, before beginning problem solving in any analytical science subject, is to list the basic laws that form the core, along with other important relations and formulas. In case of thermodynamics problems, you need to understand and note down the basic four laws of the science and the various relations that are consequences of those laws.

In fact, it is a good idea to make a comprehensive list of physics formulas, that you can use anytime.

Most important 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, and the macroscopic variables.

A knowledge of relations between these various potentials is also essential. I suggest that you make a list or table of the most important relations, which you will require, while solving problems. Understanding of theory and concepts like thermodynamic equilibrium is absolutely vital.

A knowledge of basic integration and differentiation techniques, and 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. Knowledge of probability and statistics is very useful while solving problems of statistical thermodynamics.

Make a list of the important mathematical formulas, that you require for solving most problems. You can take guidance from your instructor, regarding the mathematical techniques needed.

I cannot tell you how to solve a particular 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. 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 multiple-choice questions) meant to test your understanding of the subject.

Know the nature of the problem and proceed accordingly.

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 variables, that have been 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.

Based on the information provided, look for the equation that provides a relation between the unknown and 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.

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 the 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.