Question

The solar energy reaching the earths surface amounts to 7.0 J/(cm^2 x s). If 0.25% of this light (wavelength = 600 nm) is used by a green leaf (20 cm^2), can 100 such leaves produce enough hexose per person, per day? Average human needs about 40 g sugar/day. Assume 12 hours of sunlight/day.

Answer 1

Energy reacing the earth surface = 7J/cm2.s

if 0.25% reaches earth =7*0.25/100 j/cm2.s=0.0175 j/cm2.s

area of leaf, leat uses energy to the tune of 0.0175*20 j/s=0.35 J/s

in 12 hours of operation = 12*60*60 seconds = 43200 sec

total energy produced in 12 hours =0.35*43200=15120 joules

Eenrgy prodices by 100 leaves =15120*100 =1512*103 joules =1.512*10⁶ joules

1 kg of sugar contains 21 Mj of energy = 21*10⁶ joules of energy

40g = 40/1000 kg =0.04 kg of sugar contains =840000 j/day=8.4*105 joules/day.

This energy is less than the energy produced by green leafs. Hence 100 leaves can produce that much energy.