Consider 60 atoms with a total amount of available energy of 4400 K, where the e

Question

Consider 60 atoms with a total amount of available energy of 4400 K, where the energy is given as E/k_b, distributed in a system of equally spaced energy levels. Several possible distributions are given here as: a.) Compute the energy of each set. Which of the sets is not at the same temperature? b.) For each set, calculate the total number of possible arrangements or configurations for each distribution. Which is most probable? c.) Which of the sets is Boltzmann? d.) What is the temperature of this system? Examining these results, observe that the most probable distribution that satisfies the constraints given is the Boltzmann ensemble.

Explanation / Answer

a)The total energy for set A is given by 3x300+9x200+17x100+31x0

So, EA = 900+1800+1700 = 4400K

The total energy for set B is given by 4x300+8x200+16x100+32x0

So, EA = 1200+1600+1600 = 4400K

The total energy for set C is given by 5x300+7x200+15x100+33x0

So, EA = 1200+1600+1600 = 4400K

The total energy for set D is given by 5x300+7x200+17x100+31x0

So, EA = 1500+1400+1700 = 4600K

Set D is not at the same temperature

b) 60 atoms are distributed in various states.

So the Macrostates for each set is given by W = N!/ n1!n2!n3!n4!

Hence the no. of macrostates for set A = 60!/ 3! 9!1 7! 31!

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