Question

2.51. The energy content of the proven reserves of coal, oil and gas has been estimated to be 36 x 1021 J. The real reserve of fossil fuels (all fossil fuels under the earth’s surface) is often estimated as five times greater than the proven reserves.

Part I: Let’s obtain insight into the magnitude of solar energy by using a solar constant of 1368 W m-2 and the radius of the Earth’s land surface of 6.37 x 106 m. Assume that the net transmissivity of the atmosphere is 0.5, that 1% of the projected Earth’s surface is available for capturing solar radiation, and that this surface receives sunlight corresponding to the solar constant for an equivalent 6 hours per day. How many years would it take for solar radiation landing on this surface to obtain the energy equivalence of the proven reserves of fossil fuels? of real reserves of fossil fuels?

Part II. Hall and Rao (1999) has estimated that the global production of biomass by photosynthesis as 2 x 1011 tonnes of organic matter per year, which is equivalent to 4 x1021 J y-1. Annual food intake by humans has been estimated as an equivalent of 16 x 1018 J y-1. For proven reserves of coal, oil and gas, how many years of net photosynthesis – adjusted for the biomass necessary to feed humans - would it take to generate the energy equivalent of these reserves? How many years of net photosynthesis – again adjusted for the biomass necessary to feed humans - would it take to generate the energy equivalent of all fossil fuels under the Earth’s surface?

Answer 1

2.51

given, energy content of proven fossils, Eo = 36*10^21 J

Real energy of all fossil= 5Eo

i. solar constant, k = 1368 W/m^2

radius of earth, Re = 6.37*10^6 m

transmittivity, n = 0.5

land area available = A = 1% of projected land

exposure time every day, t = 6 hours

hecne time timen for energy to reach energy of proven fossil fuels is t'

t' = Eo/P

P = k*pi*Re^2*n*0.01*t

t' = 1911.4542620 days = 5.2332765559 years

ii. bio matter produced per year, E' = 4*10^21 J/year

annual food intake, E" = 16*10^18 J/year

for biomass, time required = t"

t" = Eo/(E' - E") = 9.036144578313253 years