Why is thermodynamics so hard?

boltzmannAn understanding of the second law of thermodynamics has been equated to reading Shakespeare in terms of its cultural significance [see my post entitled ‘Two Cultures‘ on March 5th, 2013].  So why do so few people understand it?

Perhaps it is the way that it is traditionally taught starting from a series of corollaries. Oops.  There is the first problem. Most students don’t know what a corollary is.  It is a statement that builds on a previous statement.

It is hard to find a simple statement of the second law of thermodynamics. There is the Clausius statement: no process is possible, the sole result of which is that heat is transferred from a cold body to hot body.  Then there is the Kelvin-Planck statement and if you really want to be confused then try the Carathéodory formulation.  You can read them at the bottom of this post to reassure yourself that they are impenetrable.  They were formulated when steam engines were the main source of energy and it is hard to see their relevance today in biology, chemistry and culture.

A more generic expression of the second law of thermodynamics is ‘entropy always increases’.  Oh, but now I’ve introduced entropy.  Entropy is a measure of disorder [see my posts entitled ‘Entropy management for bees and flights‘ on November 5th, 2014 and ‘Zen and entropy‘ on December 11th, 2013 ].  So according to the second law, the level of disorder must always increase. Boltzmann proposed that the level of disorder of a system could be quantified as a universal constant [k] multiplied by the logarithm of the number of ways [W] a system could be arranged with the same energy content.  Ok, so that’s getting complicated again.  But Boltzmann was so proud of it that it is carved on his grave stone [see picture] and the constant is known as the Boltzmann’s constant [=ratio of the molar gas constant and Avogadro’s number].

In an attempt to express the second law in everyday language, Bob and I re-wrote the second law as ‘you can’t have it just anyway you like it‘ in our book, The Entropy Vector.  In other words there always has to be some unwanted disorder created.


Statements (corollaries) of the second law of thermodynamics:

Clausius statement: no process is possible, the sole result of which is that heat is transferred from a cold body to hot body.

Kelvin-Planck statement: no process is possible, the sole result of which is that a body is cooled and work is performed.

Carathéodory’s formation: in every neighbourhood of every equilibrium state there is at least one state which cannot be accessed by an adiabatic process.



Thess A., The Entropy Principle: Thermodynamics for the Unsatisfied, Springer-Verlag, Berlin, 2011.

Handscombe RD., & Patterson, EA., The Entropy Vector: Connecting Science and Business, World Scientific Press, Singapore, 2004.

5 thoughts on “Why is thermodynamics so hard?

  1. Pingback: Cosmic heat death | Realize Engineering

  2. Pingback: Is the world incomprehensible? | Realize Engineering

  3. Pingback: Uncertainty about Bayesian methods | Realize Engineering

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.