A brass rod with thermal conductivity

PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A brass rod with thermal conductivity k=120 W/m⋅Kk=120\,\text{W}/\text{m}\cdot\text{K}, cross-sectional area 3.0×10−4 m23.0\times10^{-4}\,\text{m}^2, and length 0.40 m0.40\,\text{m} connects a heat reservoir at 200∘C200^{\circ}\text{C} to a 0.50 kg0.50\,\text{kg} aluminum block initially at 20∘C20^{\circ}\text{C}. Assume the temperature at the rod–block junction always equals the block’s temperature and that all energy conducted through the rod raises the block’s temperature. What is the block’s initial rate of temperature increase (dTdt)\left(\dfrac{dT}{dt}\right) at the moment its temperature is 20∘C20^{\circ}\text{C}? (Specific heat of aluminum: c=900 J/kg⋅Kc=900\,\text{J}/\text{kg}\cdot\text{K}.) (a) 1.4×10−2 K/s1.4\times10^{-2}\,\text{K/s} (b) 3.6×10−2 K/s3.6\times10^{-2}\,\text{K/s} (c) 7.2×10−2 K/s7.2\times10^{-2}\,\text{K/s} (d) 3.6×10−3 K/s3.6\times10^{-3}\,\text{K/s}

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