Respuesta :
Answer:
The area is 15.502 km².
The fraction is [tex]\dfrac{31}{218500}[/tex]
Explanation:
Given that,
Daily average insolation = 6 kWh/m²
Efficiency = 20%
Population = 324 million
Per capita power = 1378 watts
Area of tennessee = 109250 km²
We need to calculate the daily power required
Using given data
[tex]daily\ power=population\times Per\ capita\ power [/tex]
Put the value into the formula
[tex]daily\ power = 324\times10^{6}\times1378[/tex]
[tex]daily\ power=4.4647\times10^{11}\ watts[/tex]
[tex]daily\ power=4.4647\times10^{8}\ kW[/tex]
We need to calculate the total energy per day
Using given data
[tex]E=6\tiimes24[/tex]
[tex]E=144\ kW/m^2[/tex]
We need to calculate the out of total energy
Using energy and efficiency
[tex]E'=E\times\eta[/tex]
[tex]E'=144\times\dfrac{20}{100}[/tex]
[tex]E'= 28.8\ kW/m^2[/tex]
We need to calculate the area
Using formula of area
[tex]A=\dfrac{daily\ power}{out\ of\ energy}[/tex]
Put the value into the formula
[tex]A=\dfrac{4.4647\times10^{8}}{28.8}[/tex]
[tex]A=15.502\ km^2[/tex]
We need to calculate the fraction of Tennessee that is required to power
Using given data
[tex]fraction =\dfrac{Area}{tennessee}[/tex]
Put the value into the formula
[tex]fraction =\dfrac{15.502}{109250}[/tex]
[tex]fraction=\dfrac{31}{218500}[/tex]
Hence, The area is 15.502 km².
The fraction is [tex]\dfrac{31}{218500}[/tex]
