How can you determine if a process is possible or impossible by using the 1st and the 2nd Laws of Thermodynamics?


1 Answer 1


$\bf{Impossible}:$ A process is $impossible$ between two equilibrium states if at the beginning of the process the system and its surrounding has total $S_0$ entropy and at the end of the process the total entropy is $S_1$ $and$ $S_0 > S_1$.

three comments:

  1. between two equilibrium states: if you can define non-equilibrium entropy then there are possible generalizations to include entropy rates and non-equilibrium processes such that are centered around the idea that $internal$ entropy generation is always positive.

  2. possible vs. impossible: One can reformulate the above negative statement of "impossibility" to a positive one but not easily because, in general, not all processes are possible just because the final entropy is larger than the initial one. Ashes do not turn to gold just because the latter might have higher entropy, there are also other conservation laws besides energy.

  3. There are other that are sometimes more convenient formulations of the $impossibility$ statement. For example

     (a) the entropy of an *isolated* system cannot decrease, therefore in equilibrium  the entropy is maximum
     (b) the internal energy of a constant entropy system cannot increase and it is at a *minimum*
     (c) if a system can exchange heat only at a fixed given temperature than in 
         equilibrium its free energy must be minimum.

There are many other similar variations but are all are essentially equivalent $impossibility$ statements.

  • $\begingroup$ Wow, thank you for this great answer. I am grateful. May I ask, if it's not too much trouble, what about if it's possible? I am assuming that knowing if it's impossible you can also know it's possible if the conditions are opposite, if I am not mistaken. I am trying to relearn thermodynamics, but I seem to have forgotten. $\endgroup$
    – Qwin
    Aug 13, 2020 at 9:35
  • $\begingroup$ I am not sure how far one can go with what is possible. I said there are other conservation laws that a physical process must also observe, but I am fairly sure that if a process is possible than in a sufficiently small but finite neighborhood of that process other ones are also possible as long as the corresponding $S_0<S_1$ $\endgroup$
    – hyportnex
    Aug 13, 2020 at 9:46

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