Problem $4.$ Use the principles in the first three problems, along with the data and

assumptions listed below, to solve the following problem. If Penn State obtained $5$ MW $($for

heating and electricity$)$ from the combustion of willow biomass, how many square miles of

willow biomass would we need to harvest annually to provide enough biomass for our power

needs?

Data and Assumptions:

Conversion efficiency of biomass$-$burning power plant $=50\%$

Power plant input $=$ Useful electrical power output

conversion efficiency

$1$ kg dried wood $=20$ x $106$ Joules $1$ MW $=106$ watts

$1$ year $=3\mathrm{.}1536$ x $107$ seconds $1$ Joule $=1$ watt$$second

$1$ kg dried wood biomass$/$m$2=$ standing biomass of willow plantation

$1$ hectare $=10,000$ m$2640$ acres $=1$ mile$2$

$1$ hectare $=2\mathrm{.}47$ acres

See the problem statement for other necessary data.