The average amount of solar energy received at the earth’s surface in a certain location is approximately 1350 W/m². This energy can be used in a solar power plant, because of the reradiation of energy by the collector surface. Assume that the reradiation is described by Q = AσεT⁴, where A is the collector area, ε is the emissivity, and σ is the Stefan–Boltzmann constant (equal to 5.67 × 10⁻⁸ W m⁻² K⁻⁴).

a. Calculate the maximum collector surface temperature at which all the incident solar energy is reradiated and the emissivity is equal to 0.5. 

b. Suppose that the efficiency of the power plant equals the Carnot efficiency. If Tamb is the environmental temperature to which energy is rejected as heat and T_c is the collector temperature, determine the collector temperature at which the system should operate in order to achieve the most power output for a collector of a fixed size. Assume the environmental temperature is 25°C.