P(E)=exp(-1)P(E*) E=KkT(1+(2/K)) So the width of the P(E) graph, measured as the change in energy needed to cause P(e)to drop to exp(-1)of its maximum value divided by the value of the energy at which P(e) assumes this maximum value is (EE*)E*=(2/K)2. This width gets smaller and smaller as K increases. The primary conclusion is that as the number n of molecules in the sample grows, which, as discussed earlier, causes K to grow, the energy probability function becomes more and more sharply peaked about the most probable energy E*. This, in turn, suggests that we may be able to model, aside from infrequent fluctuations, the behavior of systems with many molecules by focusing on the most probable situation(i.e, having the energy E*)and ignoring deviations from his case It is for the reasons just shown that for so-called macroscopic systems near equilibrium, in which N(and hence K)is extremely large(e.g, N-10 to 10), only the most probable distribution of the total energy among the n molecules need be considered This is the situation in which the equations of statistical mechanics are so useful PAGE 5PAGE 5 P(E') = exp(-1) P(E*), one finds E' = K kT (1+ (2/K)1/2 ). So the width of the P(E) graph, measured as the change in energy needed to cause P(E) to drop to exp(-1) of its maximum value divided by the value of the energy at which P(E) assumes this maximum value, is (E'-E*)/E* = (2/K)1/2 . This width gets smaller and smaller as K increases. The primary conclusion is that as the number N of molecules in the sample grows, which, as discussed earlier, causes K to grow, the energy probability function becomes more and more sharply peaked about the most probable energy E*. This, in turn, suggests that we may be able to model, aside from infrequent fluctuations, the behavior of systems with many molecules by focusing on the most probable situation (i.e., having the energy E*) and ignoring deviations from this case. It is for the reasons just shown that for so-called macroscopic systems near equilibrium, in which N (and hence K) is extremely large (e.g., N ~ 1010 to 1024), only the most probable distribution of the total energy among the N molecules need be considered. This is the situation in which the equations of statistical mechanics are so useful