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Statement of a problem № 3594

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At low temperatures, say below 50 K, the thermal conductivity of a metal is proportional to the absolute temperature, that is, k = aT , where a is a constant with a numerical value that depends on the particular metal. Show that the rate of heat flow through a rod of length L and cross-sectional area A and whose ends are at temperatures T1 and T2 is given by Q = dA/2L (T1^2-T2^2 ).

Solution:
At low temperatures, say below 50 K, the thermal conductivity of a metal is prop

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