Physics

Problem

A flat wooden ceiling of a single-story house separates the living space from the unheated attic. Relevant characteristics are listed below. • Ceiling area:

25\,\text{m}^2

• Ceiling thickness:

0.20\,\text{m}

• Thermal conductivity of the wood:

0.040\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

Over the course of an 8-hour winter night, the indoor air is kept at

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

while the attic air stays at

4\,^{\circ}\text{C}

. Neglect additional insulation layers, convection, and radiation so that conduction through the wood is the only significant energy pathway. (a) Calculate the total thermal energy that passes through the ceiling during the 8-hour period. Express your result in joules. (b) Convert the energy found in part (a) to kilowatt-hours (kWh), the unit used by electric utilities. (c) The local utility charges \$0.12 per kWh. Determine the cost associated with the energy lost through the ceiling during this single night.

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