1= - W in Java Access QR in Java 1= - W 1= - WJava qr creation in javause java qr-code writer torender qrcode on java(n;)Barcode implement with javausing barcode implementation for java control to generate, create bar code image in java applications.This is the same definition as (3.52) except that we have replaced the infinitesimal element d 3r d 3p by a finite cell of volume w. Unfortunately this ensemble average is difficult to calculate. So we shall adopt a somewhat different approach, which will yield the same result for a sufficiently large system. It is clear that if the state of the gas is given, then f is uniquely determined; but if f is given, the state of the gas is not uniquely determined. For example, interchanging the positions of two molecules in the gas leads to a new state of the gas, and hence moves the representative in r space; but that does not change the distribution function. Thus a given distribution function f corresponds not to a point, but to a volume in r space, which we call the volume occupied by f. We shall assume that the equilibrium distribution function is the most probable distribution function, i.e., that which occupies the largest volume in r space. The procedure is then as follows:Bar Code decoder with javaUsing Barcode recognizer for Java Control to read, scan read, scan image in Java applications.(a) Choose an arbitrary distribution function by choosing an arbitrary set Qr Codes generation with visual c#using barcode encoding for .net framework control to generate, create qr code 2d barcode image in .net framework applications.of allowed occupations numbers. Calculate the volumes it occupies by counting the number of systems in the ensemble that have these occupation numbers. (b) Vary the distribution function to maximize the volume. Let uS denote by Q {n;} the volume in r space occupied by the distribution function corresponding to the occupation numbers {n;}. It is proportional to the number of ways of distributing N distinguishable molecules among K cells so that there are n; of them in the ith cell (i = 1,2, ... , K). ThereforeCompose qrcode in .netusing barcode creator for asp.net web forms control to generate, create qr code jis x 0510 image in asp.net web forms applications.Q {n;}Visual Studio .NET Crystal qr codes writer for .netusing barcode generating for .net vs 2010 crystal control to generate, create denso qr bar code image in .net vs 2010 crystal applications.n 1 !n 2 !n 3 ! .,. n K !Control qr data with vb.netto access qr code jis x 0510 and denso qr bar code data, size, image with visual basic barcode sdkg~l g;2Control european article number 13 image on javagenerate, create ean13 none on java projects... g;K Print barcode on javause java bar code writer todraw barcode with java(4.38)EAN / UCC - 13 generation with javause java gtin - 13 creation togenerate ean13+5 in javawhere g; is a number that we will put equal to unity at the end of the calculation but that is introduced here for mathematical convenience. Taking the logarithmControl datamatrix 2d barcode image in javause java data matrix barcodes encoding topaint gs1 datamatrix barcode with javaTHERMODYNAMICS AND KINETIC THEORY Control barcode code 128 image on javausing java toprint barcode code 128 in asp.net web,windows applicationof (4.38) we obtain log 0 {n i }Identcode barcode library on javausing java toincoporate identcode for asp.net web,windows applicationlog N! -Control qr codes data in .netto draw quick response code and qrcode data, size, image with .net barcode sdklog nil + Control gs1 - 13 data for vb.netto build ean-13 and ean 13 data, size, image with vb barcode sdkL n i log g; + constant 2d Data Matrix Barcode barcode library in word documentsusing office word toinsert data matrix 2d barcode in asp.net web,windows applicationNow assume that each n; is a very large integer, so we can use Stirling's approximation, log n;! =:: n; log n; - 1. We then have log 0 {n;} = N log N -Matrix Barcode barcode library on .netgenerate, create matrix barcode none for .net projectsL n; log nil Create barcode on visual c#using barcode creator for .net control to generate, create bar code image in .net applications.L n i log g; + constant Control pdf 417 data on word documents pdf-417 2d barcode data with microsoft word(4.39)Include code 3/9 in office excelgenerate, create 39 barcode none for excel spreadsheets projectsTo find the equilibrium distribution we vary the set of integers {n;} subject to the conditions (4.35) and (4.36) until log 0 attains a maximum. Let {ii;} denote the set of occupation numbers that maximizes log O. By the well-known method Lagrange multipliers we have~[logO{n;}] -~(a;~ln;+,8;~It:;ni)L [- (log n; + 1) + log g; ;=1(ni=iiJ (4.40)where a, ,8 are Lagrange's multipliers. Now the n; can be considered independent of one another. Substituting (4.39) into (4.40) we obtaina - ,8d ~n;Since ~n; are independent variations, we obtain the equilibrium condition by setting the summand equal to zero: log ii; = -1 + log g; - a - ,8t:; (4.41 ) ii = g.e-a-{l<,-lThe most probable distribution function is, by (4.37) and (4.41),/; =Ce-{l<,(4.42)where C is a constant. The determination of the constants C and ,8 proceeds in the same way as for (4.13). Writing /; == f(p;), we see that f(p) is the MaxwellBoltzmann distribution (4.23) for Po = o. To show that (4.41) actually corresponds to a maximum of log 0 { n i} we calculate the second variation. It is easily shown that the second variation of the quantity on the left side of (4.40), for-(~nJ2 < 0 ni We have obtained the Maxwell-Boltzmann distribution as the most probable distribution, in the sense that among all the systems satisfying the macroscopic conditions the Maxwell-Boltzmann distribution is the distribution common to the largest number of them. The question remains: What fraction of these systems have the Maxwell-Boltzmann distributions In other words, how probable is the most probable distribution The probability for the occurrence of any set of