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ella [17]
3 years ago
14

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.
Physics
1 answer:
SVEN [57.7K]3 years ago
5 0

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

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