Heat is transferred steadily through a 0.2-m thick 8 m ×4 m wall at a rate of 2.4 kW. The inner

step 1 The area over here is 8 times 4 in meter square. The length is 0 .2 meter. The hotter temperatur

Heat is transferred steadily through a 0.2-m thick 8 m ×4 m...

Heat is transferred steadily through a $0.2-\mathrm{m}$ thick $8 \mathrm{m} \times 4 \mathrm{m}$ wall at a rate of $2.4 \mathrm{kW}$. The inner and outer surface temperatures of the wall are measured to be $15^{\circ} \mathrm{C}$ and $5^{\circ} \mathrm{C} .$ The average thermal conductivity of the wall is $(a) 0.002 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$ $(b)0.75 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$ $(c) 1.0 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$ $(d) 1.5 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$ $(e) 3.0 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$

Heat is transferred steadily through a $0.2-\mathrm{m}$ thick $8 \mathrm{m} \times 4 \mathrm{m}$ wall at a rate of $2.4 \mathrm{kW}$. The inner and outer surface temperatures of the wall are measured to be $15^{\circ} \mathrm{C}$ and $5^{\circ} \mathrm{C} .$ The average thermal conductivity of the wall is
$(a) 0.002 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$
$(b)0.75 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$
$(c) 1.0 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$
$(d) 1.5 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$
$(e) 3.0 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$

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Key Concepts

Steady-State Heat Transfer

Steady-state heat transfer refers to the condition where the temperature at any given point in the system does not change over time, meaning that the heat entering any section of the material equals the heat leaving it. This assumption simplifies analysis because it allows the use of constant temperature differences and uniform thermal conductivity when applying Fourier's law to calculate the rate of heat transfer.

Fourier's Law of Heat Conduction

This law states that the rate of heat transfer through a material is proportional to the negative gradient of the temperature and the area through which the heat flows. It provides the fundamental relationship for analyzing conduction problems in engineering and physics, relating heat flux to the material's thermal conductivity, the cross-sectional area perpendicular to heat flow, and the temperature difference across the material.

Thermal Conductivity

Thermal conductivity is a material property that indicates how well a material can conduct heat. It is defined as the amount of heat that passes per unit time through a unit area of the material when there is a unit temperature gradient. This property is central to problems involving heat transfer, as it determines how quickly or slowly a material will respond to temperature differences.

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