An industrial freezer must keep the rate of thermal energy entering through a panel…

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

An industrial freezer must keep the rate of thermal energy entering through a 10 m210\,\text{m}^2 panel below 150 W150\,\text{W} when the temperature difference between the inside and outside surfaces is 30 ∘C30\,^{\circ}\text{C}. Two insulation materials are available: Material X has thermal conductivity 0.060 W/(m⋅∘C)0.060\,\text{W}/(\text{m}\cdot{}^{\circ}\text{C}) and costs 1515 dollars per square metre for each centimetre of thickness. Material Y has thermal conductivity 0.025 W/(m⋅∘C)0.025\,\text{W}/(\text{m}\cdot{}^{\circ}\text{C}) and costs 3030 dollars per square metre for each centimetre of thickness. Which choice minimizes the cost per square metre while still meeting the thermal requirement? (a) Either material costs the same for the required thickness. (b) Use Material X only. (c) Use Material Y only. (d) Neither material can meet the thermal requirement.

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