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. A. On average, how much energy does one house use during each 24 h day? Express your answer in joules. B. If light energy to electric energy conversion using solar cells is 16 % efficient, how many square miles of land must be covered with solar cells to supply the electrical energy for 200000 houses? Assume there is no cloud cover. Express your answer in square miles

Answer 1

a)energy used = power * time of consumption

= 10³x 24x60x60 = 86.4x10⁶=86.4MW

b) energy needed for 200000=2x10⁵ houses = E

E=86.4x10⁶x 2x10⁵ = 172.8x10¹¹ J

Since efficiency is 16%, so energy of incident light (E_{​​​​​i}) =E/0.16

E_{​​​​​​i}= 1.08x10¹⁴J

Since one square meter of ground can receive 20MJ,

So squre meter of land that receive E_{​​​​​​i} amount of energy =k

K=E_{​​​​​​i}/(20MJ);. K= 5.4 x 10⁶ m^{​​​​​​2}​​

since 1meter square = 3.8x10^-7

^{So land needed =2 square miles.}