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a) 1 b) N(N-1) c) N! / (N-1)! d) 2 N e) none of the above. Q1 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with one quantum of vibrational energy in the entire crystal. a) 1 b) N(N-1)

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## a) 1 b) N(N-1) c) N! / (N-1)! d) 2 N e) none of the above

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**a) 1**b) N(N-1) c) N! / (N-1)! d) 2N e) none of the above Q1 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with one quantum of vibrational energy in the entire crystal**a) 1**b) N(N-1) c) N! / (N-1)! d) 2N e) none of the above Q2 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with one quantum of vibrational energy in each of the atoms in the crystal? (N quanta total in the crystal)**a) 1**b) N(N-1) c) N! / (N-1)! d) 2N e) none of the above Q3 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with N (indistinguishable) quanta of vibrational energy all in a single atom of the crystal? (N quanta total in the crystal)**a) 1**b) N(N-1) c) N! / (N-1)! d) N! / [(N-2)! 2!] e) none of the above Q4 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 2 quanta of vibrational energy in one atom of the crystal? (2 quanta total in the crystal)**a) 1**b) N(N-1) c) N! / (N-1)! d) N! / [(N-2)! 2!] e) none of the above Q5 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 2 atoms of the crystal each excited with one quantum of vibrational energy? (2 quanta total in the entire crystal)**a) 1**b) 4 c) 6 d) 10 e) 16 Q6 Consider a perfect crystal that consists of 4 identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 2 quanta of vibrational energy? (2 quanta total in the entire crystal, arranged in any way)**a) 1**b) N(N-1) c) N! / (N-1)! d) N! / [(N-2)! 2!] e) (N+1)! / [(N-1)! 2!] Q7 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 2 quanta of vibrational energy? (2 quanta total in the entire crystal, arranged in any way)**a) 1**b) N(N-n) c) N! / (N-n)! d) N! / [(N-n)! n!] e) (N-1+n)! / [(N-1)! n!] Q8 Consider a perfect crystal that consists of N identical and distinguishable atoms. What is the statistical weight of the state of the crystal with n quanta of vibrational energy? (n quanta total in the entire crystal, arranged in any way)**remains unchanged**increases decreases Q9 Consider two crystals at different temperatures that are placed onto thermal contact with each other but insulated from the rest of the Universe. What happens to the entropy of the cooler crystal as thermal equilibrium is attained?**remains unchanged**increases decreases Q10 Consider two crystals at different temperatures that are placed onto thermal contact with each other but insulated from the rest of the Universe. What happens to the entropy of the warmer crystal as thermal equilibrium is attained?**remains unchanged**increases decreases Q11 Consider two crystals at different temperatures that are placed onto thermal contact with each other but insulated from the rest of the Universe. What happens to the combined entropy of both crystals as thermal equilibrium is attained?**remains unchanged**increases decreases Q12 Consider two crystals at different temperatures that are placed onto thermal contact with each other but insulated from the rest of the Universe. What happens to the entropy of the Universe as thermal equilibrium is attained?**remains unchanged**increases decreases Q13 Consider two crystals at different temperatures that are placed onto thermal contact with each other but insulated from the rest of the Universe. What happens to the combined statistical weights of the states of the two crystals as thermal equilibrium is attained?**a) 1**b) 6 c) 20 d) 35 e) 56 Q14 Consider a perfect crystal that consists of 4 identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 3 quantum of vibrational energy in the entire crystal?**a) 1**b) 6 c) 20 d) 35 e) 56 Q15 Consider a perfect crystal that consists of 4 identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 5 quantum of vibrational energy in the entire crystal?**a) 1**b) 6 c) 20 d) 35 e) 56 Q16 Consider a perfect crystal that consists of 4 identical and distinguishable atoms. What is the statistical weight of the state of the crystal with 4 quantum of vibrational energy in the entire crystal?**a) 70**b) 76 c) 105 d) 1120 e) 1225 Q17 Consider two perfect crystals that consists of 4 identical and distinguishable atoms. What is the statistical weight of the state of the combined system when one crystal has 3 quanta of vibrational energy and the other 5 quanta?**a) 70**b) 76 c) 105 d) 1120 e) 1225 Q18 Consider two perfect crystals that consists of 4 identical and distinguishable atoms. What is the statistical weight of the combined system with each crystal supporting exactly 4 quanta of vibrational energy?**a) 1120**b) 1225 c) 6435 d) 12870 e) 1372000 Q19 Consider a perfect crystals that consists of 8 identical and distinguishable atoms. What is the statistical weight of the combined system with the entire crystal supporting exactly 8 quanta of vibrational energy, arranged in any way?**a) 0**b) k ln (6435) c) k ln (6435/1120) d) k ln (6435/1225) e) k ln (2) Q20 Consider a two perfect crystals that consists of 4 identical and distinguishable atoms each, one with 3 quanta and one with 5 quanta of vibrational energy. What is the increase in entropy of the universe when these two crystals are brought into thermal contact?

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