In 2009, a group of environmentalists approached the Boulder City Council with a request to deny an application to continue operating the local coal-fired 200 MW power plant in order to reduce CO2 emissions. The group suggested that the coalfired power plant be replaced by a nonpolluting solar plant.
To evaluate the feasibility of their request, a steel plate is placed in sunlight in Boulder at an angle equal to the latitude. The plate is treated with a coating that has an absorptivity for solar insolation of 0.9 and an emissivity in the long-range spectral range of 0.2.
a. If the average insolation between 9 a.m. and 5 p.m. is equal to 400 W/m2 and the convective heat-transfer coefficient from the top surface of the plate is 8 W/m2 K, estimate the equilibrium temperature of the plate assuming the bottom is insulated and the effective sky temperature is 50 K.
b. If you could operate a heat engine between the plate temperature calculated in part (a) and the environment at 10°C, estimate the plate surface area required to generate power equal to the coal-fired power plant. Then comment on the result and compare it with a PV system of 12% efficiency.