A research laboratory must maintain an interior temperature of while the exterior…

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

Problem

A research laboratory must maintain an interior temperature of 20 ∘C20\,^{\circ}\text{C} while the exterior temperature on a summer day reaches 42 ∘C42\,^{\circ}\text{C}. One rectangular wall panel of area 7.5 m27.5\,\text{m}^2 is to be fabricated from rigid foam insulation whose thermal conductivity is 0.030 W m−1 K−10.030\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}. Laboratory regulations limit the steady–state heat flow through this panel to no more than 450 W450\,\text{W}. Answer the following. (a) Determine the minimum thickness of the foam panel that satisfies the heat–flow requirement. Express your answer to two significant figures. (b) If the panel thickness you found were reduced by 25%25\% due to a manufacturing error, calculate the new steady–state heat flow and state whether the panel would still meet the laboratory regulation.

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