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This question is about the change in energy results in change in entropy idea.

I used to know that entropy only depends on spatial configuration but afterwards I learnt it also depends on energy. This later dependency is a bit obscure to me.

Suppose there are two containers of equal volume filled with the same ideal gas in the same amount. In container A, mean kinetic energy of the gas is about 300J and in container B mean kinetic energy of gas is 200J. Now if we think of the container A, the mean value of kinetic energy is little bit distant from 0J compared to that of container B. So, kinetic energy of the gas particles of container B is comparatevely more closer to mean value than that of container A. I mean in case of container B more number of particles have the possibility to possess almost the same kinetic energy compared to container A.(thinking as a statistical distribution). Now for a certain spatial configuration (for example say that the gas particles formed a sphere altogether in a container) the number of arrangements of kinetic energy possessed by gas particles is more in A than B (for example permutation for assigning energy values to gas particles which formed the sphere). Is this the reason for which entropy in higher energy state is more than the lower?

Summary: the more the mean kinetic energy the more variations of kinetic energy is observed among the particles. Does this make entropy dependent on energy?

So can anyone please provide me an indication whether this idea as stated above is correct or not?

I apologize for using such wierd examples in between.

[I have asked this question in the comments section in one of my previous questions but could not elaborate my thoughts there. Mr.@Mark_Bell did help me in that query. However I need a little more clarification about that concept since I could not express what I was thinking completely back then]

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  • $\begingroup$ I don't understand what you mean when you talk about 150 J and 100 J of kinetic energy. $\endgroup$
    – Mark_Bell
    Commented Apr 12, 2021 at 17:59
  • $\begingroup$ Maybe you misunderstand kinetic energy. I don't understand what you mean when you say that the mean value is distant from 0. $\endgroup$
    – Mark_Bell
    Commented Apr 12, 2021 at 18:40
  • $\begingroup$ Basically I thought that for a greater mean value the dispersion is more compared to that of the lower value. I might have mixed up the whole thing for not having a clear idea about statistics $\endgroup$
    – MSKB
    Commented Apr 12, 2021 at 18:58

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I want to answer this question in simple terms and pointwise for a better understanding

Entropy is basically dispersal of matter at a given temperature In layman terms it is the number of ways a particular task can occur. Therefore it's just like probability or microstates(As in the textbook). It is an extensive function so it depends on the amount of gas/liquid. This is a state function so it does not depend on the route/path adopted for the process It also depends on Heat Content and heat further depends on the nature of gas(Monoatomic/diatomic/polyatomic), process and amount. It is 0 at 0K i.e. perfectly ordered Some textbook also refer to it as disorder or randomness I think all the above points will clear your doubt

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