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In the microcanonical ensemble every system has N molecules, a volume V, and an energy between E and E + ~. It is clear that the average total momentum of the system is zero. We show that it is possible to define quantities that correspond to thermodynamic quantities. The fundamental quantity that furnishes the connection between the microcanonical ensemble and thermodynamics is the entropy. It is the main task of this section to define the entropy and to show that it possesses all the properties attributed to it in thermodynamics. Let f ( E) denote the volume in f space occupied by the microcanonical ensemble:

I find Google News to be one of the best sources of news available online. By assembling stories from literally hundreds of different newspapers, magazines, and Web sites, it provides a depth of coverage that simply isn t possible from single-source sites like CNN.com (discussed in 11). Granted, Google News focuses on the top stories only, but where else can you go to read cover age from the New York Times, the Melbourne Herald Sun, and the Arabic News all on the same page While reading Google News selected headlines is nice, if you re searching for specific stories you need to use Google s Advanced News Search. You access the Advanced News Search page from the Google News page. You can use the Advanced News Search to search by a variety of parameters, as detailed in Table 6-5.

f(E) ==

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You may recall that we decided that login and logout do not meet the litmus test of being use cases because they do not provide something of value to the customer They are really part of the various HomeDirect use cases, such as Browse account balances and Transfer funds So, we somehow have to reuse the sequence of events required for login and logout

(6.10)

The dependence of f(E) on N, V, and ~ is understood. Let L(E) denote the volume in f space enclosed by the energy surface of energy E:

(6.11)

The UML notation provides "include" and "extend" relationships, which can be used to model such reuse within use cases

Option Results Sort by Find results with all of the words Find results with the exact phrase Find results with at least one of the words Find results without the words News source Location Occurrences Description Selects how many listings are displayed on

+ ~) - L:(E)

(6.12) (6.13)

w(E)

An include relationship allows you to capture a common piece of functionality in a separate use case, and then "include" the use case in another use case via the include relationship The include relationship is shown as a dependency relationship stereotyped as <<include>> See

(6.14)

8(E, V) == k log f(E)

word(s)

(6.15)

Figure 7 - 2

where k is a universal constant eventually shown to be Boltzmann's constant. To justify this definition we show that (6.15) possesses all the properties of the entropy function in thermodynamics, namely,

whose entropies are, respectively, 8 1 and 8 2 , the entropy of the total system is 8 1 + 8 2 , when the subsystems are sufficiently large. ( b) 8 satisfies the properties of the entropy as required by the second law of the thermodynamics. To show the extensive property, let the system be divided into two subsystems which have N 1 and N2 particles and the volumes V1 and V2 , respectively. * The energy of molecular interaction between the two subsystems is negligible compared to the total energy of each subsystem, if the intermolecular potential has a finite range, and if the surface-to-volume ratio of each subsystem is negligibly small. The total Hamiltonian of the composite system accordingly may be taken to be the sum of the Hamiltonians of the two subsystems:

.Yt(p, q) = .Yt1(P1' q1)

Here s a bonus secret, based on Google s Advanced News Search: Once you create a query for a specific topic, company, or newsmaker, you can book mark the first search results page in your Web browser. Every time you access this bookmark, you ll display an updated search results page contain ing the latest news stories on the specified topic. You can even put a short cut to this bookmark on your desktop and double-click it when you want up-to-date news on the topic at hand.

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