Two chunks of metal with heat capacities C 1 and C 2 , are interconnected by a rod of length λ and cross-sectional area S and fairly low heat conductivity K. The whole system is thermally insulated from the environment. At a moment t = 0 the temperature difference between the two chunks of metal equals ( Δ T) 0 . Assuming the heat capacity of the rod to be negligible, find the temperature difference between the chunks as a function of time.
Text Solution
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Δ T = ( Δ T) 0 e –αt , where α = (1/C 1 + 1/C 2 ) SK/ λ
= 
(T 1 – T 2 )
where T 1 and T 2 are temperatures of two chunks as function of time 't'.
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(T 1 – T 2 )
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