quiz1_rev_prob

quiz1_rev_prob - Quiz Review Problems 3.2 6.1 6.4 6.10...

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Quiz Review Problems: 3.2, 6.1, 6.4, 6.10 Solutions 3.2 Equalizing energies. For the two 10-particle two-state systems of Example 3.4, suppose the total energy to be shared between the two objects is U = U A + U B = 4. What is the distribution of energies that gives the highest multiplicity? For this problem, don’t make any assumptions about the starting positions of the particles (as they have in example 3.4), you just want to know how to distribute the particles in the two systems so that the total U=4. However, we can assume the systems are of the same format (the first energy level is e=0 and the second is e=1) and that there are again 10 particles in each system. And, let’s denote the number of particles in state i by n i . So, the multiplicity of each system individually is: ! 10 n !(10 n )! 1 1 W = so the total multiplicity is: ( ! 10 ) 2 ! 10 ! 10 = W tot = !(10 n , 1 A )! !(10 n , 1 B )! !(10 n , 1 A )!(4 n , 1 A )!(6 + n , 1 A )! n , 1 A n , 1 B n , 1 A We can evaluate this for all possible values of n 1,A : n 1,A W 0 210 1 1200 2 2025 3 1200 4 210 6.1 Calculating the entropy of dipoles in a field. You have a solutions of dipolar molecules with a positive charge at the head and a negative charge at the tail. When there
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This note was uploaded on 11/11/2011 for the course BIO 20.010j taught by Professor Lindagriffith during the Spring '06 term at MIT.

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quiz1_rev_prob - Quiz Review Problems 3.2 6.1 6.4 6.10...

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