A uniform sphere is supplied heat electrically at the centre
at a constant rate. In the steady state, steady temperatures
are established at all radial locations r, heat flows outwards
radial and is ultimately radiated out by the outer surface
isotropically. In this steady state, the temperature gradient
varies with radial distance r according to
(a) r⁻¹ (b) r⁻²
(c) r⁻³ (d) r⁻³/²
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Answer:
As we know that Q=−KA
dX
dT
where
dX
dT
=temperature gradient
Q=heatflow
now
A
Q
=−K
dX
dT
hence
dX
dT
∝
A
K
and for sphere area A=4πr
2
hence
dX
dT
∝r
−2
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