A collector has a gross area of 3 m². The collector is installed on a south-oriented roof surface with the tilt of 45° in Charlotte (Latitude = 35° North). The collector has one glass cover which has the solar transmittance of 0.88 at normal incidence. The collector plate's solar absorptance is 0.93 at normal incidence. Based on the gross area and water inlet temperature, the collector has the following characterization test results: FR =0.88 and UL = 6.02 W/(m²-°C). For an hour from 11 am to noon (solar time) on March 11 (n=59+11=70), the terrestrial horizontal solar radiation is Ib= 2.0 MJ/m² and la=0.8 MJ/m². During this hour, the water inlet temperature is 56°C and the ambient air temperature is 14°C. Accomplish the following (Needed two figures are attached at the end):
1) (5 pts) Calculate the angle of incidence of the beam radiation (use the midpoint of the hour)
2) (5 pts) Calculate R$_b$ for the collector face (use the midpoint of the hour)
3) (10 pts) Based on the isotropic model, calculate the amount of absorbed solar radiation in the given hour. Assume the ground reflectivity is 0.6.
4) (10 pts) Calculate the useful heat gain of the collector in the given hour