Boltzmann Equation for Entropy:
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We use the third law to identify changes in entropy in systems, surroundings, etc. Applications would be calculating delta s in terms of isothermal, isobaric, and isochoric conditions, calculating S in terms of Boltzmann's equation, and finding relationships in terms of delta s of the system, surroundings, and universe.
Yes, essentially the third law of thermodynamics is saying that at 0 degrees K, there is no vibrational, rotational, or translational entropy. The only possible entropy results from positional and residual. Thus, knowing the Boltzmann equation would come in handy when asked a question about the residual/positional entropy.
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