Consider a 10 particle two-state object with energy levels₀=0 and₁=1. The total energy of this first object isU_A=5. A second 10 particle object hasthreeenergy levels(₀=0,₁=1and₂=2). The total energy of this second object isU_B=4. The two objects are brought into thermal contact:

• What is the total energy of the system ?
• What is the multiplicity of states for the initial distribution of energies described above?
  • Multiplicity of object A = ?
  • Multiplicity of object B = ?
  • Total multiplicity = ?
• What is the multiplicity of states when one unit of energy flows from object B to object A?
  • Multiplicity of object A = ?
  • Multiplicity of object B = ?
  • Total multiplicity = ?
• What distribution of energy leads to the largest multiplicity? U_A= ? and U_B= ?
• What is the total multiplicity of this maximum multiplicity state ?

Now consider the same pair of objects, but in the case that the total energyU=12:

• What is the total multiplicity of states in the instanceU_A=3?
• What distribution of energy leads to the largest multiplicity? U_A= ?and U_B= ?
• What is the total multiplicity of this maximum multiplicity state?