microstate and macrostate ppt

Treatments on statistical mechanics define a macrostate as follows: a … A similar relation holds for any exchanged quantity. For For example, the changes in the microstate can be as small as 10 35 times than a macrostate, but there are still changes in this scale which may have no effect at the macrostate. Its multiplicity - the number of ways of choosing N↑ objects out of N : N Ω = ( ,0) 1 ( ,1) Ω = N N The macrostate is specified by a sufficient number of macroscopically measurable parameters (for an Einstein solid N and U). Lecture 9 Pg 11 Summary • The total entropy of an isolated system is maximum in equilibrium. Therefore, one macrostate may contain several different microstates. Thermodynamic probability: the number of microstates leading to a given macrostate. The multiplicity is the number of microstates in a macrostate. n 0 ! ( )!!! Degeneracy: an energy level contains more than one energy state. ( , ) ↑ ↓ ↑ ↑ ↑ − Ω = = N N N N N N N N N For a two-state paramagnet in zero field, the energy of all macrostates is the same (0). For example, consider a box containing two particles and only one quantized unit of energy (meaning it can't be divided up; it must go entirely to one of the two particles). !! 2. A microstate is a specific arrangement of the constituent parts of a system that produces an externally observable macrostate. As an analogy, consider a national presidential election. • So if two parts (1 and 2) can exchange V, equilibrium requires: This is a general equilibrium condition. The macrostates are the various possible winners of the election, and the microstates are the various combinations of ways in which the voters may cast their ballots. Entropy of an ideal gas: ≡1 (exactly one way to arrange zero objects)! Microstate: is specified by the number of particles in each energy state. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density. A single macrostate contains a very large number of microstates. It is donated by Wk where k represents the kth macrostate. A macrostate is an overview of a complex situation, whereas a microstate describes the details of how each element of the system functions. In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast to the macrostate, which characterizes plainly observable average quantities (temperature, for example), a microstate specifies all molecular details about the system, including the position and velocity of every molecule. The microstate is specified by the quantum state of each particle in a system (for an Einstein solid # of the quanta of energy for each of N oscillators) 3. A macrostate is specified by (N, N↑). With more available microstates, the entropy of a system increases.

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