Assuming the solar constant to be 1370 W/m² and the radius of the earth (supposed to be a sphere) R = 6370 km, calculate the power arriving at the top of the atmosphere and the energy received per day and per year. Electricity production was 1.8 × 10^4 TWh in 2005. Compare that number to the solar

Question

Assuming the solar constant to be 1370 W/m² and the radius of the earth (supposed to be a sphere) R = 6370 km, calculate the power arriving at the top of the atmosphere and the energy received per day and per year. Electricity production was [latex]1.8 imes10^{4}\mathrm{TWh}[/latex] in 2005. Compare that number to the solar energy arriving each day on top of the atmosphere.

Accepted Answer

The earth is seen from the sun as a disk of radius R . The power received is [latex]1370 imes\pi imes R^{2}=1.75 imes10^{17}\mathrm{W}.[/latex] The earth receives [latex]4.2 imes10^{15}\mathrm{kWh}/\mathrm{day}[/latex] or [latex]1.5 imes10^{18}\mathrm{kWh}/\mathrm{year}.[/latex] Each day the earth receives [latex]4.2 imes10^{15}\mathrm{kWh}=4.2 imes10^{6}\mathrm{TWh}.[/latex] This is 233 times the annual electricity consumption.

Question 7.1: Assuming the solar constant to be 1370 W/m² and the radius ......

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