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The Second Law

The second law of thermodynamics states that the entropy of any thermally isolated system will either increase or remain constant. At the time Rudolph Clausius first proposed this law (see [5]), there was no known connection between entropy and any well-understood microscopic concept. Clausius defined changes in entropy, tex2html_wrap_inline175 , in terms of macroscopic quantities: the transfer in energy in the form of heat, tex2html_wrap_inline177 , and the temperature, T:

equation12

When entropy is defined in this way, the second law of thermodynamics may be stated mathematically. For an isolated system,

equation15

One important implication of this is that work cannot be extracted from systems at equilibrium. In order to for a system to do work, it must be displaced from equilibrium, or have been away from equilibrium to begin with.

This law was found to have accurate and useful consequences, but no intuitive notion of what tex2html_wrap_inline175 signified was known until Ludwig Boltzmann proposed a statistical definition of entropy:

equation17

where tex2html_wrap_inline183 is the number of possible microstates the macroscopic system may be in, and k is Boltzmann's constant. tex2html_wrap_inline183 may be seen as a measure of the degree of randomness present in the state of the system. Boltzmann's definition of entropy is consistent with Clausius's understanding of entropy if heat tex2html_wrap_inline177 is the change in the energy of randomly moving particles. [9]



Eric H. Neilsen
Mon Jun 16 13:53:44 EDT 1997