Thursday, April 26, 2012

Student misconceptions about entropy

I am slowly learning that many students think that because of the second law of thermodynamics that the entropy of a system must increase in any process. They forget or ignore that this is only true for an isolated system. 
Nice counter examples at fixed temperature and pressure are
  • freezing of a liquid
  • condensation of vapour
  • slow compression of a gas
  • many chemical reactions: e.g., combination of hydrogen gas and oxygen gas to form liquid water in a fuel cell
For all of these processes the entropy of the system decreases.
These are possible because there is a net decrease in the Gibbs free energy.
The entropy of the system plus surroundings increases.

I am trying to address this by continually testing understanding of this point with online quizzes and in class "clicker" quizzes.


  1. I think I disagree. The entropy of an isolated system is non-decreasing, not increasing. An isolated system prepared in a microcanonical ensemble and left undisturbed should have constant entropy, or am I wrong? The entropy and the free energy are the same thing in a microcanonical ensemble. So, it seems hard to change the entropy without doing work on the system, in which case its not isolated. If it is prepared in an true equilibrium state, then the free energy is minimized and the entropy is maximized - globally. Neither will change spontaneously if the system is left alone. Or am I wrong?

  2. Whoops! The entropy and free energy in a microcanonical system are NOT the same, because they have different units! You have to multiply by Boltzmann's constant.

  3. You are correct. The entropy of an isolated system must never decrease. It can either stay constant or increase.
    But, the student misconception remains.