The Average Per Capita Rate of Primary Energy Use in Canada

Question

Examlex · 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.

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