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Thermodynamic properties such as internal energy and enthalpy are manifestations on a gross scale of the positions, motions, and interactions of the countless molecules comprising a macroscopic system The two theories that relate the behavior of molecules to macroscopic properties are kinetic theory and statistical mechanics These theories together represent a very large body of extra-thermodynamic knowledge, well beyond the scope of this text Our purpose here is to indicate in a very elementary fashion how the energy associated with the individual molecules of an ideal gas relates to the macroscopic internal energy of the ideal-gas state A fundamental postulate of quantum theory is that energy is quantized, that energy on the microscopic scale comes in very small discrete units Thus a macroscopic system has associated with it an enormous number of quanta of energy, which sum to determine its energy level Quantum theory specifies that the set of energy levels "allowed" to a closed system is determined by its volume This does not mean that fixing the volume of a system fixes its energy; it just determines the discrete set of energy levels permitted to it When a system is isolated (constrained from exchanging either mass or energy with its surroundings), it exists at one of the energy levels allowed to it Each energy level of a system has associated with it a number of quantum states This number g is known as the degeneracy of the level Although an isolated system exists at a particular energy level, it passes over time through all of the g quantum states characterized by this same energy A large number of quantum states is accessible to a system of given volume in equilibrium with surroundings at fixed temperature From the thermodynamic point of view, fixing T and V establishes the state of the system, including its internal energy However, macroscopic equilibrium does not imply a static situation on the microscopic scale The ceaseless motion of the molecules and their collisions with the walls of the container result in exchanges of energy with the surroundings, which cause momentary fluctuations in the energy of the system Thus the internal energy of thermodynamics is an average over the discrete set of energy levels of.

15:

'R L Rowley, Statistical Mechanics for Thermophysical Property Calculations, app 5, PTR Prentice Hall, Englewood Cliffs, NJ, 1994

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The DBMS can create a subgroup within a group in the ResultSet For example, the business unit may want to see orders organized by store, and within each store, orders are organized by product A subgroup is created by placing the name of the column used for the subgroup as the second column name in the GROUP BY clause of the query Any number of subgroups can be created, depending on the limitations established by the manufacturer of the DBMS used by your program Column names in the GROUP BY clause must be separated with a comma Listing 11-83 illustrates how to create a subgroup In this example, the ResultSet is grouped by store number, and within each store number group, a subgroup is created using the sales representative number Listing 11-84 contains the DownRow() method that is used to retrieve and display values from the ResultSet

Rule JSF Versions Parent Elements Child Elements Annotation(s) Uniqueness Constraints Value 20 behavior None None None

The following example illustrates the usage of the behavior-class element:

the allowed quantum states Statistical mechanics provides the means for arriving at the proper average value The fundamental postulate of statistical mechanics for a system of given volume in equilibrium with surroundings at fixed temperature is that the probability of a quantum state depends only on its energy, and all quantum states with the same energy have the same probability A value for the thermodynamic internal energy is found as the average of the energies of the accessible quantum states, each weighted by its probability The quantity of fundamental importance to come out of this procedure is the partition f ~ n c t i o n : ~

try { String query = new String ( " SELECT StoreNumber,SalesRepNumber, SUM(Sales) " + " FROM Sales " + " Group By StoreNumber, SalesRepNumber"); DataRequest = DatabasecreateStatement(); Results = DataRequestexecuteQuery (query); Systemoutprintln("Store SalesRep Sales"); Systemoutprintln("----- ------------"); DisplayResults (Results); DataRequestclose(); }

<faces-config> <behavior> <behavior-id> testbehavior </behavior-id> <behavior-class> comexamplejsfTestBehavior </behavior-class> </behavior> </faces-config>

where Ei is the energy of level i , gi is the degeneracy of the level, and k is Boltzmann's constant This quantity is a state function, from which all thermodynamic properties may be found once it is known as a function of T and V In particular, the internal energy is given by:

private void DownRow ( ResultSet DisplayResults ) throws SQLException { long StoreNumber; long SalesRepNumber; long Sum; StoreNumber = DisplayResultsgetLong ( 1 ) ; SalesRepNumber = DisplayResultsgetLong ( 2 ) ; Sum = DisplayResultsgetLong ( 3 ) ; Systemoutprintln( StoreNumber + " " + SalesRepNumber + " " + Sum); }

Rule JSF Versions Parent Elements Child Elements Annotation(s) Uniqueness Constraints Value 20 behavior None None None

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