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Into a textbook (it's too advanced for a school textbook, so there's nothing to be gained from trying toĪnyway, the appendix contains lots of equations, including the equation of heat diffusion. Sounds pretty impressive, and we might wonder what motivated John Wiley & Sons to allow such material
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Textbook written by a Professor of Mathematics Of course an appendix in a John Wiley and Sons, Inc. Appendix D is a restatement of the infamousĬreationist Second-Law-of-Thermodynamics argument against evolution. Which is titled "Can ANYTHING Happen in an Open System?". Towards the end of this textbook there are some appendices, and in particular there is an "The Numerical Solution of Ordinary and Partial Differential Equations". published the second edition of his textbook Granville Sewell is a Professor of MathematicsĪt the University of Texas El Paso, and last year (2005) It follows that it is quite reasonable to be dogmatic about the impossibility of a macroscopicĭecrease in entropy in a closed system, even though it is incorrect to state that any decrease So unimaginably small as to be indistinguishable from "it ain't going to happen", and then some. Much smaller than you can see with the naked eye), we are still talking about 602,300 bits.Īnd the corresponding probability of 2 -602,000 is a cube about 1/3000 of a millimetre on each side, which is Million times smaller in each direction (i.e. Even if we consider this problem with a volume which is one Which is,Īs you may notice, way more than 500 bits. Which in this case is equal to Avogadro's number = 6.02 × -23. To be in a chosen half of the original volume, i.e. It is easy toĬalculate the required entropy decrease from first principles,īecause it is the probability that each molecule will be found Of hydrogen gas in a closed cylinder, which corresponds to about 22 litres at room temperature and pressure.Ĭonsider the entropy required to compress this cylinder to half its original volume. It is very unlikely that a spontaneous decrease of entropy of 500 bits has ever occurred within a closed system.įor comparison, consider a macroscopic thermodynamic system.
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In other words, in the entire history of the observable universe, This corresponds to a little less than 500 bits. Who discovered the relationship between these two types of entropy. To properly reconcile these two notions of entropy, you have to introduce a constant, which is calledīoltzmann's constant, named after Ludwig Boltzmann, The second notion of entropy is the negative logarithm The first notion is entropy as the integral of dQ/Tįor reversible processes, where Q represents heat energy and The big achievement of statistical mechanics is the unification of two different So What Does the Second Law of Thermodynamics Really Say? Within closed systems, and that the Second Law does not prohibit these decreases, thisĪrgument will not fade into the obscurity that it deserves. Of evolution recognise that evolution does require the occurrence of entropy decreases Second-law-of-thermodynamics argument against the theory of evolution.
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It is this myth of absolute prohibition that underlies the persistence of the creationist Is a large decrease of entropy in a closed system. What it does prohibit, and here I am being loose with the meaning of the word "prohibit", One of the biggest misconceptions about the Second Law of Thermodynamics is that it prohibitsĪ decrease of entropy in a closed system.