Question

If light energy to electric energy conversion using solar cells is 12 % efficient, how many square miles of land must be covered with solar cells to supply the electrical energy for 350000 houses? Assume there is no cloud cover.

Answer 1

Complete Question

The light energy that falls on a square meter of ground over the course of a typical sunny day is about 20 MJ . The average rate of electric energy consumption in one house is 1.0 kW .

If light energy to electric energy conversion using solar cells is 12 % efficient, how many square miles of land must be covered with solar cells to supply the electrical energy for 350000 houses? Assume there is no cloud cover.

Answer:

The area is  $A = 1.26 *10^{7} m^2$

Explanation:

From the question we are told that

      The efficiency is  $\eta =$12%

      The number of houses is  $N = 350000$

       The light energy per day is $E = 20 \ MJ$

       The average rating of electric energy for a house is  $E_h = 1.0 \ k W = 1000W$

   

Generally the electric energy which the solar cells covering $1 \ m^2$ produces in a day is

       $E_s = \eta * E$

           $E_s = 0.12 * 20*10^{6}$

          $E_s = 2.4 MJ m^{-2}$

Energy for required by one house for one day is  

        $E_H = E_h * 1 \ day$  

       $E_H = 1000 * 24 * 3600$  

        $E_H = 86.4 MJ$

Energy needed for 350000 house is

      $E_z = 86.4 *10^{6} * 350000$  

     $E_z = 3.02 *10^{7} MJ$

The area covered is mathematically represented as

            $A = \frac{3.02*10^{7} \ MJ}{2.4 \ MJ m^{-2}}$

           $A = 1.26 *10^{7} m^2$