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GR9277 #63 |
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Problem
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\prob{63}
Which of the following is true if the arrangement of an isolated thermodynamic system is of maximal probability?
- Spontaneous change to a lower probability occurs
- The entropy is a minimum
- Boltzmann's constant approaches zero.
- No spontaneous change occurs.
- The entropy is zero.
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Statistical Mechanics }Maximal Probability
According to statistical mechanics, maximal probability is the sate of highest entropy---it's the peak of a Gaussian curve, the average score on a normally-curved test.
Spontaneous change to lower probability thus does not occur since maximal probability is the most stable state--one of highest entropy. Boltzmann's constant never approaches 0, however in the third law of thermodynamics, one has the entropy approaching 0 for  .
Eliminating choices, one has choice (D).
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Alternate Solutions |
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Comments |
neutrinosrule
2008-10-04 18:12:00 | if you know nothing about thermo at all, you can at least realize that A and D are opposites... It is at max probability so either it changes to a lower probability or it doesnt. This means one of these two things has to happen and either A or D has to be correct. After that, a logical next thought may be: why would an isolated thermodynamic system spontaneously change? And if you thought it would make more sense for it not to change than to change, you would get the right answer. |  | thebigshow500
2008-09-10 01:34:47 | "According to statistical mechanics, maximal probability is the state of highest entropy....since maximal probability is the most stable state--one of highest entropy." When the entropy reaches the highest, the energy state must become the most unstable, right? This sounds contradicting to me...And what does the probability refer to?
I have no idea about these concepts in Stat Mech. Is there any reference for us to study the "Maximal Probability"?
Lukav
2008-10-04 11:52:45 |
The probability is referring to the likelihood of finding the system in that particular state (given an ensemble of systems). Which is a Gaussian having its peak at the highest entropy. Entropy always tends to be increasing (imagine ice melting). I guess the wording 'becoming more random' might make a little more sense than 'becoming more unstable'
This is taken from a wiki article:
"The macroscopic state of maximal entropy for the system is the one in which all micro-states are equally likely to occur..."
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neon37
2008-10-21 00:29:12 |
So we know, entropy, ) where  is the multiplicity. Maximum entropy means maximum multiplicity. Maximum multiplicity implies maximum probability for that macrostate to occur. Thus, most stable.
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neon37
2008-10-21 01:14:12 |
So we know, entropy, where is the multiplicity. Maximum entropy means maximum multiplicity. Maximum multiplicity implies maximum probability for that macrostate to occur. Thus, most stable.
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neon37
2008-10-21 01:19:12 |
So we know, entropy, where is the multiplicity. Maximum entropy means maximum multiplicity. Maximum multiplicity implies maximum probability for that macrostate to occur. Thus, most stable.
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| | Andresito
2006-03-28 20:24:09 | "state" in first line |  |
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