Let M be the number of possible spatial cells the atoms may occupy in the bulk...

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Let M be the number of possible spatial cells the atoms may occupy in the bulk and N be the number of spatial cells on the surface. The gas consists of N atoms (just enough to completely fill the surface states). Let n be the number of atoms actually on the surface: n < N. An atom has an energy - while it is on the surface and 0 while it is in the bulk; thus E = en. M, N, and are all constants; n is a variable. M, N and n are all very large. (a) Using the microcanonical ensemble find the entropy as a function of n. (b) Derive an expression relating n to the temperature of the system. You do not have to solve the expression to find an explicit relation n= n(T). (c) Find n when T = 0 (d) Find the limit of n/N as T→ ∞ BULK STATES SURFACE STATES Let M be the number of possible spatial cells the atoms may occupy in the bulk and N be the number of spatial cells on the surface. The gas consists of N atoms (just enough to completely fill the surface states). Let n be the number of atoms actually on the surface: n < N. An atom has an energy - while it is on the surface and 0 while it is in the bulk; thus E = en. M, N, and are all constants; n is a variable. M, N and n are all very large. (a) Using the microcanonical ensemble find the entropy as a function of n. (b) Derive an expression relating n to the temperature of the system. You do not have to solve the expression to find an explicit relation n= n(T). (c) Find n when T = 0 (d) Find the limit of n/N as T→ ∞ BULK STATES SURFACE STATES

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a The entropy S as a function of n is given by the microcanonical ensemble expression S k l... View the full answer