"When the wizard
casts this spell, a jet of searing flame
shoots from his fingertips. His hands must
be held so as to send forth a fanlike
sheet of flames: The wizard's thumbs must
touch each other and the fingers must be
spread. The burning hands send out flame
jets 5 feet long in a horizontal arc of
about 120 degrees in front of the wizard"
(AD&D Player Handbook, 2nd ed, 262).
This iconic spell
(pictured to the left) has been recreated
in every edition of Dungeons and Dragons,
though it's area of effect and its damage
have changed in every edition as well.

But It's a Dry Heat
To determine the
amount of energy that this spell requires,
we first have to find it's volume. the fan
is described as a 5ft long fan, so, using
the area of an arc
:
Aarc
= π r2 ( θ / 2π )
This gives us an
area of about 26.2 ft
2.
Assuming the fan has a thickness of about
1 inch, it has a volume of 2.18 ft
3
or 0.0617 m
3.
Now that we have
a volume, we can determine the amount of
energy that the spell needs in order to be
cast. We are going to assume that the
spell is cast at standard temperature and
pressure (STP) of 0º C, and 100 kPa in dry
air. Given the color of the fire in the
official artwork,
we can place the temperature of the flames
as reaching around 1300º C.
We can now use
the the following formula to find the
thermal energy (Q) of the spell.
Q = c m ΔT
Given the
specific heat capacity (c) for dry air,
the mass (m) of the air (calculated from
our volume and the density of the air at
STP), and our change in temperature,
this version of burning hands requires
103. kJ to be transformed into thermal
energy.