Question

A solar collector receives solar radiation at a rate of 0.315 kW per m²and delivers the heat to a storage unit whose temperature remains a constant 500 K. A power cycle receives heat from the storage unit, generates electricity at the rate of 570 kW and discharges heat to the atmosphere (20°C). For operation at steady state, calculate the theoretical minimum solar collector area required.

Answer 1

Answer:

4370.83044 m²

Explanation:

$W_{net}$ = Net work done = 570 kW

$T_l$ = Low temperature resrvoir = 20 °C

A = Area of solar collector

Amount of solar heat received = $Q_h$ = 0.315A

$\eta_{th}=\eta_{Carnot}=1-\frac{T_l}{T_h}\\\Rightarrow \eta_{th}=1-\frac{20+273}{500}\\\Rightarrow \eta_{th}=1-0.586\\\Rightarrow \eta_{th}=0.414$

$\eta_{th}=\frac{W_{net}}{Q_h}\\\Rightarrow Q_h=\frac{W_{net}}{\eta_{th}}\\\Rightarrow Q_h=\frac{570}{0.414}\\\Rightarrow Q_h=1376.81159\ kW$

$Q_h=0.315A\\\Rightarrow A=\frac{Q_h}{0.315}\\\Rightarrow A=\frac{1376.81159}{0.315}\\\Rightarrow A=4370.83044\ m^2$

The theoretical minimum solar collector area required is 4370.83044 m²