Suppose that the entropy of a certain substance (not an Einstein solid) is given by S = a(E)^1/2, where a is a constant. What is the energy E as a function of the temperature T? (Use the following as necessary: a and T.)

On a mild saturday morning while people are working inside, the furnace keeps the temperature inside the building at 23degreesc. at noon the furnace is turned off, and the people go home. the temperature outside is a constant 16degreesc for the rest of the afternoon. if the time constant for the building is 3 hr, when will the temperature inside the building reach 18degreesc? if some windows are left open and the time constant drops to 2 hr, when will the temperature inside reach 18degreesc?