The average solar flux incident on a horizontal surface in t

The average solar flux incident on a horizontal surface in the United States (averaged over 24 hours and 365 days) is about 180^2 W/m [57.06 Btu/ h ft^2 ]. How much land would be needed to supply the total energy demand of the United States, approximately 80X10^18 J (76 quad) per year, by means of photovoltaics (efficiency around 10%) and biomass (efficiency around 1%)? Compare with the land area of the United States, 9.16106 km2 (3.54X10^6mi2 ).

Solution

Solar PV

Average solar flux = 180 W/m²

Considering 1 m² surface the energy available from sun per year = 180x3600x24x3600 = 5.676 x10⁹ J/year

Energy requirement of US per year= 8x10¹⁸  J/year

Considering energy conversion efficiency of 10 %

Total energy available after conversion per m² =(Energy available)X(conversion efficiency) = 5.676x10⁹x0.1 = 5.676x10⁸ J/year

Hence land requirement =(Energy required per year after conversion)/(Energy available per year per m² after conversion)= 8x10¹⁸/5.676x10⁸ = 1.409x10¹⁰ m²

=14100 km²

Land area of USA = 9.16x10⁶ km²

Hence required land for solar energy is= (Required land for plant)/(Total available area)= 14100/9.16x10⁶ = 0.0015363

Or

0.154 % of available land

Bio Mass

Assuming combined efficiency of energy conversion by bio-mass vegetation and the power plant is 1 % and using the same amount of incident solar radiation (180 W/m²)

Energy available for use after conversion per m² of area = (Energy available) x (efficiency) =5.676x10⁹x0.01 = 5.676x10⁷ J/year

Hence required land area = (Required energy after conversion per year)/(available energy after conversion per m² per year) =8x10¹⁸/5.676x10⁷ = 1.409x10¹¹ m²

=141000 km²

Which is 1.54% of available land area in US