Engineers are testing two flat aluminum plates, Plate X and Plate Y
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Engineers are testing two flat aluminum plates, Plate X and Plate Y, that are identical in every respect except surface finish. Each plate has area 0.060m2, thickness 4.0mm, and is initially at a uniform temperature of 120∘C. The plates are quickly moved into a large laboratory room held at 20∘C with still air (no forced convection).
• Plate X has a dull, oxidized surface with emissivity εX=0.88.
• Plate Y is highly polished, giving εY=0.04.
The edges are insulated so that energy leaves only through the two large faces of each plate. The thermal conductivity of aluminum is 2.3×102W⋅m−1⋅K−1.
(a) Describe qualitatively how the temperature within each plate will vary with time during the first few minutes after being placed in the room. Account for the roles of both conduction inside the plate and radiation from its surfaces.
(b) Derive an expression for the initial rate of energy loss from Plate X in terms of given quantities and fundamental constants. Clearly state any approximations you invoke.
(c) Using your result from part (b) and additional reasoning, determine which plate will reach 60∘C first. Quantitatively estimate the ratio of their initial cooling rates.
(d) After a long time, both plates approach thermal equilibrium with the room. Explain why the total time required for the plates to cool differs less dramatically than the initial cooling-rate ratio might suggest.