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Microstate and Macrostate (Read 4303 times)
Gerrit-Jan Linker
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Microstate and Macrostate
30.01.11 at 20:42:11
Microstate and Macrostate
  • Macrostate
    A macrostate is the thermodynamic state of any system that is exactly characterized by measurement of the system's properties such as P, V, T, H and number of moles of each constituent.  
    Thus, a macrostate does not change over time if its observable properties do not change.  
  • Microstate
    a microstate for a system is all about time and the energy of the molecules in that system. "In a system its energy is constantly being redistributed among its particles. In liquids and gases, the particles themselves are constantly redistributing in location as well as changing in the quanta (the individual amount of energy that each molecule has) due to their incessantly colliding, bouncing off each other with (usually) a different amount of energy for each molecule after the collision.. Each specific way, each arrangement of the energy of each molecule in the whole system at one instant is called a microstate."

A microstate is a full specification of all degrees of freedom of a system. A system may be conveniently defined as having N degrees of freedom confined to a volume V. In general, microscopic degrees of freedom are quantum numbers. The index i in the following equation runs over all unique combination of quantum number values. There is a spectrum of energy eigenstates for any system given by
where H is the Hamiltonian, |i> is shorthand (``ket'' notation) for the system wavefunction in state i, and Ei is the energy of state i. In contrast to model systems usually considered in elementary quantum mechanics, the number of distinct microstates of systems of 10^{23} particles that have the same energy E is very large, and this set of eigenstates is in practice impossible to obtain explicitly. This is indeed why we must instead treat this set statistically. We refer to the number of states that satisfy a given energy as the degeneracy of the energy level, denoted Omega(E,N,V):
Omega(N,V,E) = number of microstate with N and V energy between E+dE.
The many ``equivalent'' states numbering Omega(N,V,E) is called a microcanonical ensemble.  
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« Last Edit: 30.01.11 at 21:36:49 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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