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QPages 98-102: Q13: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q13 Solution: Figure shows water in a container having 2.0 mm thick walls…

Figure shows water in a container having 2.0 mm thick walls made of a material of thermal conductivity 0.50 W m−1 �C−10.50 \text{ W m}^{-1} \text{ �C}^{-1}. The container is kept in a melting-ice bath at 0�C. The total surface area in contact with water is 0.05 m20.05 \text{ m}^2. A wheel is clamped inside the water and is coupled to a block of mass M as shown in the figure. As the block goes down, the wheel rotates. It is found that after some time a steady state is reached in which the block goes down with a constant speed of 10 cm s−110 \text{ cm s}^{-1} and the temperature of the water remains constant at 1.0�C. Find the mass M of the block. Assume that the heat flows out of the water only through the walls in contact. Take g=10 m s−2g = 10 \text{ m s}^{-2}.

Step-by-Step Verified Solution

**Answer:** Mass M = 12.5 kg. **Step-by-Step Explanation:** Given: thickness = 2 mm = 2 _ 10__ m, K = 0.50 W m__�C__, A = 0.05 m_, _T = 1�C, v = 0.1 m/s, g = 10 m/s_. Power from falling block = Mgv. Heat flow rate = K A _T / l = 0.50 _ 0.05 _ 1 / (2 _ 10__) = 12.5 W.
Mgv=12.5⇒M×10×0.1=12.5⇒M=12.5 kgMgv = 12.5 \Rightarrow M \times 10 \times 0.1 = 12.5 \Rightarrow M = 12.5 \text{ kg}
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