Consider a collection of N localized particles, each of which can be in one of 2
ID: 2018492 • Letter: C
Question
Consider a collection of N localized particles, each of which can be in one of 2 states. Let the states be denoted 1 and 2 with energies denoted 1 and 2. The system is in thermodynamic equilibrium at Temperature T.
A. What is the number of ways that n1 particles can be found in the state with energy 1.
B. Write an expression for the partition function of the collection.
C. What is the average energy of the collection as a function of , where =1/kT.
D. What is the average number of particles in state 1 when the system is at tempature T?
E. Write an expression for entropy of the collection and evaluate the entropy in the temperature limits T=0 and T approaching infinity.
Explanation / Answer
A) number of ways that n1 particles can be found in the state with energy 1 total number of particles is N W = N! / n1 ! total number of particles is N B) partition function of the collection is Z = e -1 + e -2 c) Average energy of the collection as a function of is E = ( - 1 / Z ) ( dZ / d ) = ( - 1 /Z ) d/ d ( e -1 + e -2 ) = ( 1 / Z ) ( 1 e -1 + 2e -2 = ( 1 e -1 + 2e -2 ) / e -1 + e -2 d) average number of particles in state 1 when the system is at tempature T n1 / N = e -1/kT / ( e -1 + e -2 )Related Questions
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