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QPages 98-102: Q36: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q36 Solution: Figure shows two adiabatic vessels, each containing a mass m of …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the heat flow as affecting only one vessel, writing dΔT/dt = -KAΔT/(m s L) and thus obtain t = (msL/KA)ln2. In reality both masses change temperature, giving dΔT/dt = -2KAΔT/(m s L); the extra factor 2 must be included to avoid a 2× error in the time constant.

Figure shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.

Step-by-Step Verified Solution

**Answer:** t = (msL/KA) ln 2. **Step-BY-Step Explanation:** For two vessels connected by a rod, the temperature difference decays exponentially. Time for difference to become half: t = (msL/KA) ln 2 where m is mass of water in each vessel.

All Questions in this Chapter

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