# Energy minimisation, confusion in interpretation of question

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1. Feb 15, 2016

### Dazed&Confused

Perhaps not an appropriate place to ask this. I've completed a question which is phrased as the following:

Explain, on thermodynamical grounds, why the minimisation of the energy $E(S, V, N)$ yields the equilibrium state of a system with fixed entropy S, volume V and number of particles $N$.

I had one interpretation, to show that minimisation of the energy, i.e. that $dE = 0$, leads to a fixed entropy, volume, and number of particles.

The correct interpretation was actually to show that under fixed, entropy, and number of particles the energy is minimised, using the second law. To me, this does not make sense, however it did lead to one question: is there a situation where minimising $E$ would lead to a constant entropy, volume, and number of particles where this was not specified initially?

2. Feb 15, 2016

### Simon Bridge

... that's how I read it. The state is given by the numbers (S,V,N).

... what would the constraint be? Minimum energy could be zero for zero particles.

3. Feb 16, 2016

### Dazed&Confused

Ok thanks. Ignore my question.

What I do not understand is why if $E(S,V,N)$ does constant $S, V, N$ not mean constant $E$.

I've seen the derivation using the availability but I'm not sure why the supposed contradiction isn't one.

Last edited: Feb 16, 2016