A 1 GWe wood burning generating station operates at a Carnot efficiency of $30 \%$ and has a capacity factor of $75 \%$. What is the mass of wood required annually? What is the volume in $\mathrm { m } ^ { 3 }$ of this wood?

Question

Quizplus · Accepted Answer

The Answer is A 1 GWe generating facility with a capacity factor of 75% will produce a total
energy per year of

( 0.75 ) imes \left( 1.0 imes 10 ^ { 9 } \mathrm {~W} ight) imes \left( 3.15 imes 10 ^ { 7 } \mathrm {~s} / \mathrm { y } ight) = 2.36 imes 10 ^ { 16 } \mathrm {~J} / \mathrm { y }

At a Carnot efficiency of

30 \%

this represents a total thermal energy of

\left( 2.36 imes 10 ^ { 16 } \mathrm {~J} / \mathrm { y } ight) / ( 0.3 ) = 7.87 imes 10 ^ { 16 } \mathrm {~J} / \mathrm { y }

Since the energy content of wood is

1.4 imes 107 \mathrm {~J} / \mathrm { kg }

, then the annual wood required is

\left( 7.87 imes 10 ^ { 16 } \mathrm {~J} / \mathrm { y } ight) / \left( 1.4 imes 10 ^ { 7 } \mathrm {~J} / \mathrm { kg } ight) = 5.63 imes 10 ^ { 9 } \mathrm {~kg} / \mathrm { y }

Since the density of wood is

5.0 imes 10 ^ { 2 } \mathrm {~kg} / \mathrm { m } ^ { 3 }

(Table 8.6) then the volume of wood required is

\left( 5.63 imes 10 ^ { 9 } \mathrm {~kg} / \mathrm { y } ight) / \left( 5.0 imes 10 ^ { 2 } \mathrm {~kg} / \mathrm { m } 3 ight) = 1.125 imes 10 ^ { 7 } \mathrm {~m} ^ { 3 } / \mathrm { y }

This is a cube about

\sim 220 \mathrm {~m}

on a side.

A 1 GWe Wood Burning Generating Station Operates at a Carnot