Answer:
2377.35 km
Explanation:
Given the following;
1. A cornfield is 1.5% efficient at converting radiant energy into stored chemical potential energy;
2. The conversion from corn to ethanol is 17% efficient;
3. A 1.2:1 ratio for farm equipment to energy production
4. A 50% growing season and,
5. 200 W/m2 solar insolation.
As per our assumptions,1.2/1 is the ratio for farm equipment to energy production,
So USA need around 45.45% (1/(1+1.2) replacement of fuel energy production which is nearly about = 0.4545*10^{20} J/year = \frac{0.4545*10^{20}}{365*24*3600}=1.44121*10^{12} J/sec
Growing season is only part of year ( Given = 50%),
Net efficiency = 1.5%*17%*50%=0.015*0.17*0.5=0.001275 = 0.1275%
Hence , Actual Energy replacement (Efficiency),
=\frac{1.44121*10^{12}}{0.001275} = 1.13*10^{15} J/sec=1.13*10^{15} W
As per assumption (5),
\because 200 W/m2 solar insolation arequired,
So USA required corn field area = 1.13*10^{15}/200 = 5.65*10^{12} m^{2}
Hence, length of each side of a square,
= (5.65*10^{12} )^{0.5} = 2377.35 km
