You have three blocks of different materials at various temperatures. they are 2

Question

You have three blocks of different materials at various temperatures. they are 2-kg block of iron at 600 K, a 3-kg block of copper at 800 K, and a 10-kg block of granite at 300 . The heat capacities are .460(iron), .385(copper), and .790(granite) in kJ/(kg K), all independent of temperature. For solids, the heat capacities at constant pressure and constant volume can be assumed to be equal. What is the maximum amount of work that can be extracted from heat interactions between these blocks? No heat interactions with the environment are allowed. You do not need to describe the details of the process that produces the maximum work, but you do need to describe the final state of the blocks fully.

Explanation / Answer

this is not the proper way to do the problem. If the amount of work was equal to the heat transferred then there would by a change in entropy of the universe. you have to operate under the idea that the change in entropy must be zero. so mcpln(T/800)(Copper)+mcpln(T/600)(Iron)+mcpln(T/300)(Granite)=0. solve for T and you will get 358.268K. Use this value to determine the amount of heat lost by the iron and copper. The absolute value of the heat lost by the iron and copper minus the heat gained by the granite equals the amount of work extracted. When using this method the amount of work extracted will be positive, depending on the sign convention you are dealing this, you may have to make it negative.

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