Understanding Entropy: Calculations and Examples for Beginners

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Entropy is fundamentally understood as a measure of disorder, which tends to increase over time, except at absolute zero. The discussion highlights the calculation of entropy using the formula S = -k·Σ[Pilog(Pi)], where k is the Boltzmann constant and Pi represents the probability of a particle being in a specific nanostate. Participants seek clarity on how to apply this formula, particularly in determining probabilities and interpreting the results in terms of energy units like J/K. A deeper understanding of entropy is linked to its role in thermodynamics and information theory, emphasizing its significance in energy distribution within a system. Overall, the conversation aims to demystify entropy calculations and their implications for beginners in physics.
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Hi guys! I'm new to the forum and had several questions about entropy. I am a bit of a physics newbie by a lot of standards but I understand a lot of it and love physics. I can understand the basics of entropy that it is (correct me if I'm wrong) basically just disorder, that it is always increasing except if it is at absolute 0. It creates an arrow of time in the way that we can't go back on what has happened and bring the order back just as we can't reverse time to stop a volcanic eruption. Now I get the principles of it but how is it calculated and what does it mean when it is? there are the more basic forumula's for thermodynamics but I was referring to
S=-k·Σ[Pilog(Pi)]. So I know what most of it means,
k=boltzmann constant,
Σ = sigma,
in the brackets = the probability that a particle will be in a certain nanostate * by the logarithm of the same probability.
but how is this applicable? I want an example. I tried to do one by myself but i was most likely horribly wrong on what to do.
So i'd like an example with the math written out and what it means really. how do you know the probability of a particle being in a nanostate? once you have the number what's the unit in... J/K^-1? and what does it mean if you have a higher entropy?
sorry for the bombardment of questions... I'm just trying to wrap my head around this
 
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Thanks a ton.. this really helped!
 
Sorry about reviving, but I've thought of entropy as, well, sort of information.
 
yeah... I've got a better handle on it now. One good definition I read was "the amount of energy needed to complete a system." that's where it all just clicked for me I guess
 
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