A thermoelectric unit consists of n cells. When there is no temperature difference across the leads, the resistance is 4 ohm. Kg is 0.3 W/K. When the unit is submitted to a 80 K temperature differential, it generates a 1.71 V across a 3 ohm load. To simplify the problem, make the unrealistic assumption that alpha, R, and K are temperature independent. Determine the current that pumps 10 W of thermal energy from 300 K to 350 K. Defining the COP of a thermoelectric heating system as the ratio of the delivered thermal energy to the electric power. Determine the COP of the device when extracting thermal energy from an environment at 300 K and delivering thermal energy at 350 K. Express the COP as a function of I. Determine the current that optimizes the COP. Note: To optimize do not take derivatives, but instead use numerical solutions. Determine the amount of thermal energy pumped under conditions in part (c).