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السلام عليكم ورحمة الله وبركاته

المسألة الأولى
Assume that in the problem shown in Figure 2.3, the single particle
energy level of subsystem 2 which has an energy of 4 units is two fold degenerate. Show that the total number of microstates accessible to the composite closed system is increased from 84 to 96 and the ensemble average energy of subsystem 2 at thermal equilibrium




المسألة الثانية
Isolated system A has non-degenerate single particle quantum energy levels of energy 0,2,4,6,8,10 energy units and consists of one red particle of spin zero having an energy units. Isolated system B has non-degenerat single particle quantum energy levels of energy o,1,2,3,... 10 energy units, and consists of two non-interacting particles of spin zero, coloured white and blue respectively. The total energy of the white and the blue particles is 2 energy units. List the microstates accessible to each isolated system. The two system are placed in thermal contact. What is the number of microstates accessible to the composite system? What is the increase in entropy? Calculate the ensemble averages of the energies of both system after they are placed in thermal contact.
Repeat the calculations for the case when the particle are identical bosons of spin zero.


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