An apparatus of spherical shell type of the radius s of a few mm having uniformly distributed point heat sources on its surface is used for measuring thermal conductivity.
The thermal conductivity is given by the equation
k=
q0/4πθ·1/
s_??_
on the assumption of no heat loss, Θ∞ being the temperature rise of the center of the shell after infinite time, q
0 the heat input per unit time.
Correction for the heat loss through the lead wires of the heater and thermocouples is performed by the equation
k_??_
k+
b√
km, where
km is the thermal conductivity by the aforementioned equation assuming no heat loss,
k the true conductivity and
b a certain constant of the apparatus. This equation is derived by the condition of heat conservation
q0=
ql∞+
q∞ at infinite time where
ql∞ is the heat loss through leads and
q∞ the heat input to the shell, both per unit time.
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