Journal of Physics Special Topics
P3 8 Burning tropical trees
B.S.Chima, K.Tassenberg, B.M.Lloyd, N.Wall
Department of Physics and Astronomy, University of Leicester. Leicester, LE1 7RH.
November 19, 2015.
Abstract
This article investigates whether the energy produced from the estimated biomass of tropical trees on
Earth is equivalent to that produced by the Sun for an hour. It was found that the tropical trees can only
support the output energy of the Sun for 1.338 × 10−9 seconds.
Introduction
The Earth’s natural resource of trees has been used
by mankind for many generations. The early cavemen discovered its use for making fires and providing
warmth when the Earth’s position was not facing the
Sun. In this article we investigate the trees in the tropics (tropical areas of the world, such as America, Asia
and Africa) by determining their estimated average total biomass and analyse whether this would provide the
same energy as the Sun would for one hour.
using the Stefan-Boltzmann law
Pr = e4πRs2 σTs4 .
(1)
Where, Pr is the power radiated outwards from the
star, Rs is the radius of the Sun, Ts is the surface
temperature on the star and σ, is Stefan’s constant
at 5.8 × 10−8 W m−2 K−4 and e is the emissivity of
the radiating surface. The emissivity of the Sun is 1
because it radiates like a perfect black-body, [4].
This power output of the star can be converted to energy output, E, over a given specific time using Eq.
(2),
This is interesting because for a longer period of time,
would Earth’s trees be able to have enough biomass
from these trees to sustain the Sun’s energy for an
hour, or even a day? The burning of trees is taken
for granted compared to harnessing nuclear power in
many less economic areas of the world. The energy
produced from a nuclear power station is much more
beneficial to our climate compared to using trees as a
fuel source in these countries.
dE
,
dt
Where, t, is the time taken.
P =
(2)
Analysis and Results
The available biomass for burning is 9.863 × 1013 kg
Theory
and wood gives 22 MJ kg−1 of energy per kilogram
Firstly, we consider the estimated total biomass from
of biomass. So multiplying these values we find that
the tropics. It is found to be 1.9706 × 1014 kg [1]. This
the biomass of tropical trees that is used for burning
was calculated by adding the undisturbed, logged and
releases 2.168 × 1021 J of thermal energy.
non-productive trees for the total tropics presented on
page 17, table 7 of the referenced article.
Using Eq. (1) and a Sun’s surface temperature as 6000
K with the Sun’s radius of 6.96×108 m, we find that the
power output is 4.5×1026 W. Using Eq. (2) the energy
released from the power output can be calculated.
50% of a tree’s dry biomass is estimated to be carbon
compounds, primarily in the form of cellulose, see ref.
[2] and this is where the energy will be provided from
when trees are burned. So, its good practice to use this
when we determine the available biomass to produce
energy. Therefore, the available biomass is 9.853×1013
kg, for burning.
If we divide the total thermal energy produced from the
tropical trees by the Sun’s power output we calculate
1.338 × 10−9 seconds.
Discussion
Clearly, this indicates how powerful the sun is and that
it would lose a lot of mass every second. If we assumed
that the entire mass of Earth was converted to energy using the Einstein energy-mass relation, E = mc2 ,
then it still would not be enough to power the sun for
a second. Theoretically, this equation would not work
Burning wood is a chemical reaction which releases a
set amount of energy each time. So we assume that
the efficiency of this process is perfect at 100%, hence
we take the maximum value of about 22 MJ kg−1 [3].
Next we calculate how much power the Sun produces
1
Burning tropical trees, November 19, 2015.
this way because it is for relativistic energies and relativistic masses.
For future workings on this article, a greater variety
of trees can be selected. Tropical trees were the focus
of this report because we assumed that the majority
of the trees mass are found here and there are many
articles on the internet that support this assumption.
Furthermore, if all the trees in the tropics were burnt
then the oxygen level in the planet would decrease substantially. There would be a substantial increase in the
green house effect. Therefore, it is a possibility that life
on Earth would be strongly affected by this and could
lead to life extinction.
In addition to this, an extension task to this article
would be to consider the feasibility of burning this
large amount of wood or all of the trees on the planet
with respect to the area required. Consequently, future work into the damage provided to the environment from burning all these trees in a short period of
time.
Conclusion
It is clear that the trees in the tropical forests would
not be able to sustain the same amount of energy as
the Sun. Not for an hour and not even for a second.
In fact, from this estimated data of Ref. [1] we find
that the energy from the biomass of these tropical trees
would power the sun for only 1.338 × 10−9 seconds.
Further research in the effects mentioned in the discussion section of this article are needed for a clearer idea
on the climate change effects due to the burning of all
of the tropical trees at the same time.
References
[1] Sandra Brown, Andrew Gillespie and Ariel E. Lugo.
Biomass estimation methods for tropical forests with
applications to forest inventory data. Forest Science,
35:881–902, 1989.
http://www.researchgate.net/
profile/Sandra_Brown10/publication/233643575_
Biomass_Estimation_Methods_for_Tropical_
Forests_with_Applications_to_Forest_Inventory_
Data/links/00b495287f997262cd000000.pdf.
[2] Sylva Foundation. OneOak project. http://sylva.
org.uk/oneoak/tree_facts.php, Accessed: 26 October, 2015.
[3] University of Washington.
Energy Numbers.
http://www.ocean.washington.edu/courses/
envir215/energynumbers.pdf, Accessed:
26 October, 2015.
[4] Paul Allen Tipler and Gene Mosca. Physics for scientists and engineers with Modern Physics. W.H. Freeman, 2007.
2