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

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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/m3.

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