Two metal blocks of equal mass M of the same substance, one at an initial temperature Tⁱ₁ and the other at an initial temperature Tⁱ₂, are placed in a well-insulated (adiabatic) box of constant volume. A device that can produce work from a flow of heat across a temperature difference (i.e., a heat engine) is connected between the two blocks. Develop expressions for the maximum amount of work that can be obtained from this process and the common final temperature of the blocks when this amount of work is obtained. You may assume that the heat capacity of the blocks does not vary with temperature.