A laboratory technician needs to keep three cylindrical solid samples at a constant…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A laboratory technician needs to keep three cylindrical solid samples at a constant room temperature of 25∘C. Each sample has length 0.10m and cross-sectional area 3.0×10−4m2. One end of each sample is held in contact with a thermal reservoir maintained at 95∘C, while the other end is exposed to room air so that energy leaves only through the sample itself. The three samples are made of different materials:
• Sample A: aluminum, thermal conductivity kA=2.3×102W⋅m−1⋅K−1
• Sample B: brass, kB=1.1×102W⋅m−1⋅K−1
• Sample C: pine wood, kC=0.12W⋅m−1⋅K−1
Assume the temperature of each sample remains uniform along its length except for a steady linear gradient between the two ends.
(a) Rank the three samples according to the rate at which energy is transferred from the hot reservoir through the sample to the room, from greatest to least. Clearly indicate any ties.
(b) Provide a qualitative explanation for your ranking in part (a) that refers explicitly to relevant physical properties or relationships.
(c) The technician replaces Sample C with a second piece of pine wood that has twice the cross-sectional area and the same length as before. Predict how the energy-transfer rate through this new wooden sample compares to that of Sample B, and justify your answer without using any numerical calculation.