# Question: most of the heat supplied by a fireplace to a...

###### Question details

Most of the heat supplied by a fireplace to a room is through
radiation. Suppose a wood fire heats up to 600°C while
in use. Let’s approximate the wood fuel as a cylinder
with a 20 cm radius and a height of 60 cm. Use these
dimensions to find the total surface area, and for simplicity
assume this total value for the duration of the fire (don’t worry
about the fireplace geometry or how the log disintegrates while
burning). Assume an emissivity of *ε*
=0.95. How much radiant energy is provided by the fire
over one hour? If the log burns down completely over the
hour, how does this value compare with the total heat content of
the wood? Hardwood has a lower heating value of 13.5 MJ/kg and a
density of 750 kg/m^{3}.