The heat flow through a hollow sphere of thermal conductivity ,k, with inner radius, ri and outer radius ro and with the internal temperature maintained at Ti and the external temperature maintained at To is given by:
Male Emperor penguins need to incubate their eggs
for at least 60 days throughout the Antarctic winter. Penguins need to
maintain a body temperature of 39°C. Emperor penguins have a layer
of air, trapped by feathers that is about 3cm thick which provides the
primary source of thermal insulation. During the incubation period the
penguins use up their fatty body reserves to provide warmth. If the mean
temperature is -55°C, estimate the mass loss of an Emperor penguin
while it is incubating its egg.
You may approximate an Emperor penguin as an insulated
sphere with internal radius 25cm and outer radius 28cm. The thermal conductivity
of the insulating layer is 0.03 WK -1 m-1 and the
calorific value of penguin fat is 37500 kJkg-1.
With thanks Pete Barham
