Consider that you have a 10kg iron block at temperature T1 = 500 K placed in a room with temperature T0 = 300 K. The outside temperature is 275 K. The specic heat of iron is 0.45 kJ / kg K (according to Wolfram Alpha). a) Find the heat added to the room if the iron block is allowed to cool without doing anything else. 1)) Find the maximum possible work that can be extracted from the rst kJ of heat that is extracted from the iron block. c) Find the temperature change dT in the block from extracting a small amount of heat, Q. Evaluate o'T for Q = 1 lo]. (1) As the block gives heat to the room, its temperature decreases, so the maximum extractable work decreases. Find the maximum total work that can be performed by extracting all of the heat on cooling the block to T0. This will require setting up and performing an integral. Assume the heat capacity does not depend on temperature. e) What is the total heat given to the room by cooling the block if the work extracted from the block is used to run a Carnot heat pump, bringing in heat from outside? Compare your answer with part a