Recent content by tom26

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    Loss of motivation when research becomes 9-5 job.

    I'm 6 months into a PhD (admittedly in Chemical Engineering, not physics, but my project has a modelling bent) and, as the title suggests, I've been struggling to find motivation day in and day out. It's silly: give me an interesting problem in a project not related to my work (say a math...
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    The Fundamental Assumption of Statistical Mechanics

    You probably understand this by now, but to answer your second question, the reason it's very unlikely to be found in a state in which all of the atoms are in one corner is that there are (relatively) few of those states, compared to the number of homogeneous ones. The simple analogy is tossing...
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    Exercises in Statistical Mechanics

    I'm enjoying Lennard Susskind's lectures on Statistical mechanics. I've briefly studied this material before, but I've learnt a lot about more practical calculations from these lectures: he's used the partition function to derive all sorts of fun expressions, and to analyse the ideal gas and a...
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    Calculus Gelfand & Fomin vs. Lanczos to learn Calculus of Variations

    The benefit of Gelfand and Fomin is that everything is rigorous. It is presented clearly, and there's really very little uncertainty in what they are saying. You'll read the first 100 pages and know all you need to know about the Calculus of Variations. It is a lovely book. I read Lanczos a few...
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    Calculus Why "Transition Books (Apostol, Spivak)" are necessary?

    If you're self-studying real analysis, make sure you check out the videos of Francis Su's course at Harvey Mudd College. He's a wonderful teacher, and his course covers the first 5 chapters of Rudin. Personally, I'm not a huge fan of these intermediate books. I found real analysis on the line...
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    Foundations Naive Set Theory by Halmos

    This remains one of my favourite math texts. It gives you the language of sets and relations, functions and cartesian products, equivalence classes and 'the axiom of choice', plus a little more advanced set theory, in an easily digested format. You'll also understand Russell's paradox in a new...
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    Justification of generalisation from reversible processes to all procesess

    Thanks, I think that finally all makes sense, it all seems so simple now :) . It all works because the equation is only referring to changes of state functions within the system. Irrespective of what process is used to get from A to B, the changes in entropy, etc. will be the same. However, for...
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    Justification of generalisation from reversible processes to all procesess

    Thanks for your help! What you say makes a lot more sense. But given that, what does wikipedia mean when they say: "...This equation has been derived in the case of reversible changes. However, since U, S, and V are thermodynamic functions of state, the above relation holds also for...
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    Justification of generalisation from reversible processes to all procesess

    Hi all, I've been having some difficulty understanding the derivation of the Fundamental Theorem of Thermodynamics, dU=T \ dS-P \ dV. The derivation, which can be found at Wikipedia (http://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation) first starts with the universal First Law...
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