Engineers are designing a composite panel consisting of a layer of material A bonded…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Engineers are designing a composite panel consisting of a layer of material A bonded to a layer of material B. During a transient manufacturing step, each layer will independently absorb the same amount of thermal energy Q. The engineers want the two layers to experience identical temperature rises so that thermal stresses at the interface remain small. Relevant properties are as follows.
Material Specific heat (J kg⁻¹ °C⁻¹)
A 4.50×10²
B 9.00×10²
(a) Derive an expression for the required ratio mAmB of the masses of the two layers that will produce equal temperature rises when each layer absorbs the same energy Q. Express your result solely in terms of the given specific heats.
(b) If the mass of layer A must be 2.0 kg for mechanical reasons, determine the mass that layer B should have according to your expression from part (a).
(c) Suppose instead that the panel were fabricated with 1.0 kg of each material. Determine which layer would experience the greater temperature rise and by what factor relative to the other layer.
(d) Discuss how an unequal temperature rise during the manufacturing step could lead to mechanical failure in service, even if the panel later operates at a uniform temperature.