### Thermodynamics: A Tour through the Three Laws

Thu ,18/02/2021I’m not sure how they got to be laws, but they do appear inviolable in most instances.

**The First Law:** “Energy is conserved, i.e.,
it can be neither created nor destroyed.”

However, it may change from one form to another, such as heat to work. This law allows you to trace energy as it changes from one form to another and to identify all the places it ends up in the environment.

It was a little embarrassing when atomic physicist discovered you could convert mass to energy. Before that, there was also a Law of Conservation of Mass. However, the amount of energy produced is given by Einstein’s Law: E = mC^{2}. So mass is now considered to be another form of energy and energy is considered to be another form of mass. It is difficult to convert energy to mass, but then, again, there is the Creation Story.

**The Second Law:** “It is impossible to
convert heat completely into work.” …Lord Kelvin

There are many different statements of the second law, all supposedly equivalent, although it may take several pages of equations to show it. The second law of thermodynamics was originally an empirical observation about the workings of heat engines. It was later realized that it was a fundamental law of nature, and it was most useful as it introduced the concept of entropy (S).

“In an isolated system, a process can occur only if it increases the total entropy of the system.” … Rudolph Clausius

One very useful derivation based on the second law is that for an engine converting heat to work, the :

Maximum
Efficiency = ( T_{h} – T_{c} ) / T_{h}

Here, T_{h} is the higher operating temperature of the engine and T_{c} is the colder temperature of the exhaust. Using this we can show that the maximum efficiency of a coal-fired power plant is about 35%, while an extension of the formula shows the maximum efficiency of an internal combustion engine is about 15%. This, for instance, means that an electric car reduces carbon emissions by about half – even if charged from a coal-fired power plant.

Chemists have found entropy very useful as it can be used predict whether a chemical reaction will be spontaneous and how much product will be produced when equilibrium is reached, as:

”The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.”

With the advent of quantum mechanics, a better understanding came of how entropy relates to individual particles. Particles tend to arrange themselves in their energy levels in such a way as to reach a minimum in energy and a maximum probability. Which arrangement of particles below is more probable?

A B

Clearly, B is more probable as there are more ways to arrange the particles in the energy levels. The relationship between entropy and energy is made clear in this model. To move from arrangement A to arrangement B will require energy to move the particles up in the energy levels. The entropy of each arrangement can be calculated by:

S = kln(W)

where k is Boltzmann’s constant and W is the number of ways the set of particles may be arranged in the energy levels. Arrangement A is very interesting as there is only one way, and S= kln (1) = 0. That would be the arrangement at 0° Kelvin, and that leads us to the Third Law.

**The Third
Law**: “*As the temperature of a system
approaches absolute zero, all processes cease and the entropy of the system approaches
a minimum value.”*

In other words, at 0° Kelvin ( –273 ^{o}C),
all particles are in their lowest energy states. At that temperature, all motion ceases,
except for the vibration of molecules and the motion of electrons, and those
energies are in their lowest possible states. Attempts to achieve 0° K have
been unsuccessful, as cooling an object requires extracting energy from it and
depositing it somewhere cooler. And, there is nowhere cooler. The lowest
temperature achieved has been a little less than 1 billionth of a degree
Kelvin, which is cold enough for most purposes.

It is convenient to have an absolute scale with which to measure thermodynamic properties, as absolutes are otherwise hard to find. I once witnessed an argument between a colleague, called barracuda Beth by students, and a humanities professor about whether there were absolutes. My colleague won the argument by claiming that the atomic weight of oxygen-16 was absolutely 16 amu, and humanities professor had no come back. Unfortunately, she picked the wrong absolute. The next year, the standard for measuring mass was changed to carbon-12, and oxygen became 15.995 amu. Wisely, I did not mention that to my colleague, and that also explains the first sentence in this article.

Note: I have somewhat simplified the laws of thermodynamics and have avoided mathematical equations as much as possible. The goal was to give you a feeling for the laws and to entertain you. I hope you find it interesting.

© 2021 – J. C. Moore All rights reserved.