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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

Two adiabatic vessels, as shown in the figure, each contain a mass m of water at different temperatures. A metal rod of length L , area of cross section A , and thermal conductivity K has its ends inserted into the water. Determine the time required for the temperature difference between the vessels to drop to half of its initial value. The specific heat capacity of water is s . Assume the heat capacity of the rod an

Options

  1. AKA 2Lms 2
  2. B2Lms KA 2
  3. CLms KA 2
  4. DLms 2KA 2

Correct answer

D. Lms 2KA 2

Step-by-step solution

Let T₁ and T₂ be the temperatures of the water in the two vessels at time t , with T₁ > T₂ . The rate of heat flow through the metal rod from the hotter vessel to the colder vessel is given by: dQ dt = KA(T₁ - T₂) L The heat lost by the first vessel causes its temperature to decrease, while the heat gained by the second vessel causes its temperature to increase. The rates of change of their temperatures are: dT₁ dt = - 1 ms dQ dt dT₂ dt = 1 ms dQ dt Let the temperature difference be T = T₁ - T₂ . The rate of change

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