(a) Calculate the rate of heat conduction through house...

(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is 120 $\mathrm{m}^{2}$ and their inside surface is at $18.0^{\circ} \mathrm{C}$ , while their outside surface is at $5.00^{\circ} \mathrm{C}$ . (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?

Key Concepts

Fourier's Law of Heat Conduction

Fourier's Law states that the rate of heat transfer through a material is directly proportional to the temperature difference across it and the area through which the heat flows, and inversely proportional to the thickness of the material. This law provides the fundamental equation to calculate the heat conduction rate, namely Q/t = kA(?T/?x), which is applicable in evaluating energy losses in building envelopes.

Thermal Conductivity

Thermal conductivity is an intrinsic property of a material that measures its ability to conduct heat. Higher thermal conductivity indicates more efficient heat transfer, while lower conductivity suggests better insulating properties. This parameter is critical in selecting building materials to control energy loss in thermal applications.

Temperature Gradient

The temperature gradient is the spatial rate of change of temperature within a material. It drives the heat conduction process, as a larger temperature difference over a given distance results in a higher rate of heat transfer. Understanding this concept is essential for assessing energy efficiency in building design.

Geometric Factors in Conduction

The geometry of the material, particularly its cross-sectional area and thickness, plays a crucial role in determining the rate of heat transfer. A larger surface area allows for more heat to be transferred, whereas a greater thickness reduces the rate of conduction, affecting the overall insulation performance of a building.

Electrical Heating Power Requirements

Calculating electrical heating power requirements involves determining the amount of energy that must be supplied to balance the heat loss due to conduction. This concept connects the thermodynamics of heat transfer with practical energy needs, guiding the sizing and number of heating units necessary to maintain desired indoor temperatures.

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