A laboratory technician must choose the thickness of a polystyrene foam panel that…

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

Problem

A laboratory technician must choose the thickness of a polystyrene foam panel that will be installed between an experimental chamber at

37\,^{\circ}\mathrm{C}

and the surrounding room, which is held at

22\,^{\circ}\mathrm{C}

. The panel will have an exposed area of

2.0\,\mathrm{m^{2}}

. The experiment protocol specifies that the rate of thermal energy transfer into the room must not exceed

75\,\mathrm{W}

. The thermal conductivity of the foam is

0.030\,\mathrm{W\,m^{-1}\,^{\circ}C^{-1}}

. (a) Determine the minimum panel thickness that satisfies the protocol requirement. (b) The technician discovers that only panels with thicknesses that are integer multiples of

2.5\,\mathrm{cm}

are commercially available. Identify the smallest commercially available thickness that meets the requirement and calculate the corresponding rate of thermal energy transfer. (c) Discuss qualitatively how the required thickness would change if the temperature of the chamber were reduced while the allowable transfer rate remained the same.

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