Answer to Question #243307 in Molecular Physics | Thermodynamics for gglok

Question

A solar powered heat engine designed to receive heat from a solar collector plate and rejects heats to the surrounding atmosphere that is at 30 °C. When a concentrating collector is used the plate operate at a surface temperature of 250 °C while when a flat plate collector is used the plate has an operating temperature at 90 °C. From experiments, it was found that for the concerned location the maximum possible solar heat received is about 1880 kJ/m2 h. Find the change in minimum area required for a change from flat plate to concentrating collector if in both cases the heat engine need to generate 1 kW of useful shaft power

Answer 1

$\frac WS=\sigma (T_1^4-T^4),$

$\frac W{S+S_0}=\sigma (T_2^4-T^4),$

$S_0=\frac W{\sigma}(\frac 1{T_2^4-T^4}-\frac 1{T_1^4-T^4})=0.9~m^2.$