Question

The sun transfers energy to the earth by radiation at a rate of approximately 1.00 kW per square meter of surface.

a.If this energy could be collected and converted to electrical energy with 24 efficiency how large an area (in square kilometers) would be required to collect the electrical energy used by the United States? ( joules per year).

b.If the solar collectors were arranged in a square array, what would be the length of its sides in kilometers and in miles?

please help with all parts

Answer 1

1320336992.2512 m²

1320.33 kilometers or 509.79 miles

Step-by-step explanation:

Energy transferred by the sun

`W=0.24* 1* 10^3=240\ W/m^2`

Energy required by the United States is
`1* 10^(19)\ J/yr` (assumed)

Power

`P=(E)/(t)\\\Rightarrow P=(1* 10^(19))/(365.25* 24* 3600)\\\Rightarrow P=316880878140.2895\ W`

Area

`A=(P)/(W)\\\Rightarrow A=(316880878140.2895)/(240)\\\Rightarrow A=132033699.2512\ m^2`

Area of the solar collector would be 1320336992.2512 m²

Converting to km²

`1\ m^2=(1)/(1000* 1000)\ km^2`

`1320336992.2512\ m^2=1320336992.2512* (1)/(1000* 1000)\ km^2=1320.33\ km^2`

Converting to mi²

`1\ m^2=(1)/(1609.34* 1609.34)\ mi^2`

`1320336992.2512\ m^2=1320336992.2512* (1)/(1609.34* 1609.34)\ mi^2=509.79\ mi^2`

Each side of the square would be 1320.33 kilometers or 509.79 miles