Earth\'s atmosphere contains 550 parts per billion H 2 by volume. (a) Estimate t

Question

Earth's atmosphere contains 550 parts per billion H2 by volume. (a) Estimate the total volume of the atmosphere, approximating it as a uniform layer 60 km thick. (b) Use section 11,2's figure of 12.8 MJ/m3 to estimate the total chemical energy content of atmospheric hydrogen. (c) If we could do the impossible and extract all that hydrogen with minimal energy expenditure, how long would it power human civilization at our current energy-consumption rate of 18TW?

294 CHAPTER 11ENERGY CARRIERS: ELECTRICITY AND HYDROGEN World China France United States Other 5% Other 3% Other 5% Fossil 890 Hydro 7% Other 6% Hydro 17% Hydro 18% Hydro 11% Nuclear Nuclear 19% Nuclear 2% Fossil 67% Fossil 68% Fossil 11% Nuclear California lowa New Hampshire Other 5% Biomass 8% Solar 5% Wind 2% Wind 7% Geothermal Wind 29% Hydro 6% Hydro 8%- Fossil 31% Hydro 2% Nuclear 7% Fossil 61% Fossil 62% Nuclear 52% Nuclear 8% FIGURE 11.2

Explanation / Answer

a) For calculating total volume of atmosphere, we can simply calculate the volume of earth along with the atmosphere and then subtract the volume of solid earth from this.

The radius of the earth is 6371 km and thickness of the atmosphere is assumed to be 60km so combined radius will be 6431 km.

Now the volume of atmosphere= volume of earth along with the atmosphere- volume of solid earth={ (4/3)×?× combined radius^3}- {(4/3)×?× radius of solid earth^3}={(4/3)×?×6431^3}-{(4/3)×?×6371^3}= (4/3)×?×(6431^3-6371^3)= 3.089×10^10 cubic km =3.089×10^19 cubic metres

b) The energy content of hydrogen is 12.8 MJ/ m^3 , the percentage of hydrogen in atmosphere is 0.000055 % and the volume of atmosphere as calculated above is 3.089×10^19 cubic metres. So the total chemical energy of atmospheric hydrogen = energy content of hydrogen×percentage of hydrogen in atmosphere× volume of atmosphere= 12.8×0.000055×3.089×10^19 MJ= 2.17×10^16 MJ

c) If we extract all the energy from atmospheric hydrogen it will be 2.17×10^16MJ.

The rate of consumticon=18 TW= 18×10^6MJ /sec

So, the duration of time total energy of atmospheric hydrogen will be used= Total energy of atmospheric hydrogen/ rate of consumption =2.17×10^16/18×10^6 =1.205×10^9 seconds = 382.2791 years.

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