Let us approximate a large compost pile as a half of a sphere, and assume it is sitting

on well$-$insulated ground so that you can actually model the pile as a complete sphere

$($there is no heat flux into the ground$).$ The pile has a radius of $2$ m $.$ Look up the

thermal conductivity of soil in your book and use that for compost. The outside of

the pile is subject to convection of the wind with $T_{}=20C$ and $h=25\frac{W}{m^2}-C.$

a$)$ What level of heat generation due to microbial action is needed to get the inside

center of the pile to $80$ C $?$

b$)$ Plot the temperature of the pile from the inside to the outside.

c$)$ If weed seeds are killed if the temperature is over $60$ C $,$ what percentage of the

pile is killing weed seeds?

Those who have worked with compost piles know that they need to be turned every so

often to expose all material to the higher temperatures.