A solid copper rod of uniform cross-sectional area and length is used to conduct…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A solid copper rod of uniform cross-sectional area 3.0×10−4 m23.0\times10^{-4}\,\text{m}^2 and length 0.50 m0.50\,\text{m} is used to conduct energy from a steam reservoir at 150 ∘C150\,^{\circ}\text{C} to an ice bath held at the melting point. Assume no significant energy losses except through the rod. The setup is allowed to run steadily for 10.0 minutes. Useful data: • Thermal conductivity of copper: 400 W m−1 K−1400\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1} • Latent heat of fusion for ice: 3.3×105 J kg−13.3\times10^{5}\,\text{J}\,\text{kg}^{-1} (a) Determine the total amount of thermal energy conducted through the rod during the 10.0-minute interval. (b) Calculate the mass of ice that completely melts as a result of the conducted energy. (c) If the cross-sectional area of the rod were doubled while all other parameters remained the same, explain qualitatively and quantitatively how the mass of ice melted in 10.0 minutes would change.

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