The average thermal conductivity of the walls (including the...

The average thermal conductivity of the walls (including the windows) and roof of the house depicted in Figure $\mathrm{P} 20.67$ is $0.480 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C},$ and their average thickness is $21.0 \mathrm{cm} .$ The house is heated with natural gas having a heat of combustion (that is, the energy provided per cubic meter of gas burned) of $9300 \mathrm{kcal} / \mathrm{m}^{3} .$ How many cubic meters of gas must be burned each day to maintain an inside temperature of $25.0^{\circ} \mathrm{C}$ if the outside temperature is $0.0^{\circ} \mathrm{C}$ ? Disregard radiation and the energy lost by heat through the ground.

Key Concepts

Thermal Conductivity

Thermal conductivity is a material property that measures a material's ability to conduct heat. It quantifies the rate at which heat energy passes through a material from a region of higher temperature to a region of lower temperature, making it a central parameter in analyzing heat transfer through building components such as walls and roofs.

Fourier's Law of Heat Conduction

Fourier's Law of heat conduction describes the relationship between the heat transfer rate through a material, the material's thermal conductivity, the area through which heat is flowing, the temperature difference across the material, and its thickness. This law is crucial for calculating the energy loss through the construction elements of a building under steady-state conditions.

Heat Loss Calculation in Buildings

Heat loss calculation involves estimating the energy (or power) that escapes from a building due to conduction, which is a direct result of the temperature difference between the inside and outside surfaces of the building envelope. This calculation helps in determining the heating energy required to maintain a comfortable indoor temperature.

Energy Content of Fuels

The energy content of fuels, often expressed as the heat of combustion, indicates the amount of energy released when a given volume or mass of fuel is burned. In the context of building heating, this concept is used to relate the energy required to overcome heat loss and the volume of fuel needed to supply that energy, ensuring efficient energy management.

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