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

4370.83044 m²

Step-by-step 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-(T_l)/(T_h)\\\Rightarrow \eta_(th)=1-(20+273)/(500)\\\Rightarrow \eta_(th)=1-0.586\\\Rightarrow \eta_(th)=0.414`

`\eta_(th)=(W_(net))/(Q_h)\\\Rightarrow Q_h=(W_(net))/(\eta_(th))\\\Rightarrow Q_h=(570)/(0.414)\\\Rightarrow Q_h=1376.81159\ kW`

`Q_h=0.315A\\\Rightarrow A=(Q_h)/(0.315)\\\Rightarrow A=(1376.81159)/(0.315)\\\Rightarrow A=4370.83044\ m^2`

The theoretical minimum solar collector area required is 4370.83044 m²