where EA and EB are the thermal energies of systems A and B. If the two solids are brought to thermal equilibrium, what relation, if any, can be made between the final energies EA,f and EB,f?
9. Consider a very strange system whose multiplicity is ̐A = 1 regardless of how much energy it has. Imagine starting this system with some amount of energy and bringing it into thermal contact with system B, an Einstein solid.
(a) In which direction will the energy flow, or will no energy flow?
(b) What can you say about the energies of the final state? For example, will they be equal? If they are unequal, which is larger? Is there anything more you can conclude?
10. A substance has entropy S = c∘Etherm, where c is some constant. Use the definition of temperature to find Etherm as a function of T.
11. Consider two Einstein solids with NA = 3 and NB = 3 and eight energy units.
(a) Make a table like Table 9.2. Note that many of the multiplicities you will need are already in Table 9.2, so there is no need to re-calculate everything.
(b) How many times more probable is the macrostate with equally shared energy than the macrostate where system A has all the energy?
12. An Einstein solid has four oscillators and three units of energy.
(a) Calculate the multiplicity of the solid.
(b) Identify all the possible microstates using the parenthesis notation of Example 1.
