Two adiabatic vessels, each containing the same mass m of water at different temperatures, are connected by a rod of length L , cross-section A and thermal conductivity K . The rest of the rod is insu

Question

Two adiabatic vessels, each containing the same mass m of water at different temperatures, are connected by a rod of length L , cross-section A and thermal conductivity K . The rest of the rod is insulated and its heat capacity is negligible. The specific heat of water is s . The temperature difference between the two vessels reduces to e 1 ​ of its original value after a time Δ t . The thermal conductivity of the rod may be expressed by:

TestHub · Accepted Answer

Each vessel obeys m s d t d T ​ = ± L K A Δ T ​ , so d t d ( Δ T ) ​ = − m s L 2 K A ​ Δ T . The difference falls to e 1 ​ when m s L 2 K A Δ t ​ = 1 , so K = 2 A Δ t m s L ​ . D.

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