A solar energy power plant consists of a carnot engine with a cold reservoir maintained at 40 degree celcius using river water, and a hot reservoir maintain at temperature T by focusing sunlight onto a 1 m2 exposed area with emissivity = 1. The whole of the rest of the system is thermally lagged. the sunlight is collected and focused by an array of mirrors of total area 90 m2. The engine extracts a power of 35.5kW from the hot reservoir. Assuming that the only other heat loss from the hot reservoir is by radiation from the exposed area, calculate the temperature T. Hence calculate (i) the efficiency and power output of the engine, (ii) the power in the cooling water and (iii) the overall efficiency of the system.
[The solar flux is 1kWm-2 at the earth's surface and the Stefan-Boltzmann constant,σ is 5.67 x 108Wm-2K-4]