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Microstates and Thermodynamic States The state of a system is an important concept in thermodynamics and is defined as the complete set of all its properties which can change during various specified processes. The properties which comprise this set depend on the kinds of interactions which can take place both within the system and between the system and its surroundings. Any two systems, subject to the same group of processes, which have the same values of all properties in this set are then indistinguishable and we describe them as being in identical states. A process in thermodynamics is defined as a method of operation in which specific quantities of heat and various types of work are transferred to or from the system to alter its state. As we pointed out, one of the objectives of thermodynamics is to relate these state changes in a system to the quantity of energy in the form of heat and work transferred across its boundaries. In discussing non-thermodynamic processes, a system may be chosen as a single ultimate particle within a larger quantity of matter. In the absence of chemical reactions the only processes in which it can participate are transfers of kinetic or potential energy to or from the particle. In this case we would like to relate these energy transfers to changes in the microstate of the system. A microstate for this one-particle system is a set of coordinates in a multi-dimensional space indicating its position and its momenta in various vector directions. For example, a simple rigid spherical monatomic molecule would require a total of six such coordinates, three for its position and three for its momentum in order to completely define its microstate. Now consider a system containing a large number of these ultimate particles. A microstate of this system is a set of all position and momentum values for all the particles. For example, if there were N rigid spherical molecules we would then need 6N coordinates to give a complete set of all the microstate properties and define a microstate for this system. In a multiparticle system a particular microstate exists only for an instant and is then replaced by another so that there is no experimental way to measure the set of positions and motions which comprise one microstate among the vast number of them which occur sequentially. Because the microstates of a multiparticle system represent exactly what all the particles are doing, all thermodynamic properties of the group are thus determined by them. With this common origin all the thermodynamic properties are therefore related to each other and we need to develop this relationship. The set of all the thermodynamic properties of a multiparticle system its temperature, pressure, volume, internal energy, etc., is defined as the thermodynamic state of this system. An important aspect of this relationship between thermodynamic properties is the question of how many different thermodynamic properties of a given equilibrium system are independently variable. The number of these represents the smallest number of properties which must be specified in order to completely determine the entire thermodynamic state of the system. All other thermodynamic properties of this system are then fixed and can be calculated from these specified values. The number of these values which must be specified is called the variance or the degrees of freedom of the system. |
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