The average per capita rate of primary energy use in Canada is approximately 13 kW. Spruce trees grow at an average rate of approximately 0.005 kg per m² of forest per day and have an average energy content of $1.7 \times 10 ^ { 7 } \mathrm {~J} / \mathrm { kg }$ (a) If all energy in Canada were generated from spruce trees with the same average efficiency as present energy sources, what is the area of spruce forest needed to satisfy one person's energy needs?
(b) What is the area of spruce forest needed to provide all of Canada's population with energy? What fraction of the total land area does this represent?

Question

The average per capita rate of primary energy use in Canada is approximately 13 kW. Spruce trees grow at an average rate of approximately 0.005 kg per m² of forest per day and have an average energy content of

1.7 \times 10 ^ { 7 } \mathrm {~J} / \mathrm { kg }

(a) If all energy in Canada were generated from spruce trees with the same average efficiency as present energy sources, what is the area of spruce forest needed to satisfy one person's energy needs?
(b) What is the area of spruce forest needed to provide all of Canada's population with energy? What fraction of the total land area does this represent?

Quizplus · Accepted Answer

The Answer is (a) The growth rate may be written as

\left. \left( 0.005 \mathrm {~kg} / \left( \mathrm { m } ^ { 2 } \cdot \mathrm { d } ight) ight) / ( 86400 \mathrm {~s} / \mathrm { d } ) = 5.79 imes 10 ^ { - 8 } \mathrm {~kg} / \left( \mathrm { m } ^ { 2 } \cdot \mathrm { s } ight) ight)

Since the energy content of the wood is

1.7 imes 10 ^ { 7 } \mathrm {~J} / \mathrm { kg }

the growth represents the storage of energy at a rate of

\left( 5.79 imes 10 ^ { - 8 } \mathrm {~kg} / \left( \mathrm { m } ^ { 2 } \cdot \mathrm { s } ight) ight) imes \left( 1.7 imes 10 ^ { 7 } \mathrm {~J} / \mathrm { kg } ight) = 0.984 \mathrm {~J} / \left( \mathrm { m } ^ { 2 } \cdot \mathrm { s } ight) = 0.984 \mathrm {~W} / \mathrm { m } ^ { 2 }

So for an average per capita primary power consumption of

13 \mathrm {~kW}

then the area required per capita to obtain the same primary energy from spruce trees is

\left( 1.3 imes 10 ^ { 4 } \mathrm {~W} ight) / \left( 0.984 \mathrm {~W} / \mathrm { m } ^ { 2 } ight) = 1.32 imes 10 ^ { 4 } \mathrm {~m} ^ { 2 }

(b) For a total population of

35.8

million the total land area to obtain all primary energy from spruce trees is

\left( 3.58 imes 10 ^ { 7 } ight) imes \left( 1.32 imes 10 ^ { 4 } \mathrm {~m} ^ { 2 } ight) imes \left( 10 ^ { - 6 } \mathrm {~km} ^ { 2 } / \mathrm { m } ^ { 2 } ight) = 4.73 imes 10 ^ { 5 } \mathrm {~km} ^ { 2 }

Note that the total land area of Canada is

9.985 imes 10 ^ { 6 } \mathrm {~km} ^ { 2 }

so providing all energy with spruce trees will require about

100 imes \left( 4.73 imes 10 ^ { 5 } \mathrm {~km} ^ { 2 } ight) / \left( 9.985 imes 10 ^ { 6 } \mathrm {~km} ^ { 2 } ight) = 4.7 \%

although much of the land area is in the arctic and not appropriate for tree growth.

The Average Per Capita Rate of Primary Energy Use in Canada