- #1
shockingpants
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Hi,
I just completed a semester of undergrad course in thermodynamics/stat mech and while I find it somewhat easy to simply dump the right equations in different situation to get the right answer, its the fundamentals that has continued to baffle me. I shall be as concise as I can and hopefully, someone will be able to shed light on my queries.
Please correct anything I state if its unclear or just plain wrong!
This is my understanding of a microcanonical ensemble. It is an ensemble where every accessible state of an isolated system has a total energy (between E and E+ΔE). I shall define these states to be micro states as well. By the ergodic hypothesis, given enough time and/or systems, each of these states will have an equal chance of being sampled. In fact, this only applies at equilibrium since different microstates share the same probability only at equilibrium. (AKA, the equal a priori probability postulate only holds at equilibrium) If I assume that the number of states do not depend on any other parameter, then the total number of states Ω[itex]_{tot}[/itex] does not change, i.e. entropy of the system is constant.
If this is right thus far, I shall move on to talk about the canonical system, where my questions really lie.
I just completed a semester of undergrad course in thermodynamics/stat mech and while I find it somewhat easy to simply dump the right equations in different situation to get the right answer, its the fundamentals that has continued to baffle me. I shall be as concise as I can and hopefully, someone will be able to shed light on my queries.
Please correct anything I state if its unclear or just plain wrong!
This is my understanding of a microcanonical ensemble. It is an ensemble where every accessible state of an isolated system has a total energy (between E and E+ΔE). I shall define these states to be micro states as well. By the ergodic hypothesis, given enough time and/or systems, each of these states will have an equal chance of being sampled. In fact, this only applies at equilibrium since different microstates share the same probability only at equilibrium. (AKA, the equal a priori probability postulate only holds at equilibrium) If I assume that the number of states do not depend on any other parameter, then the total number of states Ω[itex]_{tot}[/itex] does not change, i.e. entropy of the system is constant.
If this is right thus far, I shall move on to talk about the canonical system, where my questions really lie.
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