On a very still morning, the surface temperature of a lake used to cool the condenser of a power plant is \(30^{\circ} \mathrm{C}\) while the air temperature is \(23^{\circ} \mathrm{C}\) with a relative humidity of \(80 \%\). Assume a surroundings temperature of \(290 \mathrm{~K}\). The lake is nominally circular in shape with a diameter of approximately \(5 \mathrm{~km}\). Determine the rate of heat loss from the surface of the lake by radiation, free convection, and evaporation. This heat loss determines the capacity of the lake to cool the condenser. Justify why the heat transfer correlation you select is useful, even though \(R a_{L}\) is outside of its specified range.