Final answer:
The question requires calculating the heat current through a wall using the sum of thermal resistances of its layers. For an ideal wall, a simple sum of R factors is used. Realistically, adding wood studs changes the R value calculations due to their different thermal properties and area coverage.
Step-by-step explanation:
The question at hand involves calculating the rate of heat flow through a wall that incorporates multiple layers each with its own thermal resistance (R factor). The formula used for calculating heat flow rate (heat current) in steady state conditions is given by:
Q = ΔT / Rtotal
where:
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- Q is the heat current (rate of heat flow)
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- ΔT is the temperature difference across the wall
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- Rtotal is the total thermal resistance of the wall
For part (a), the total thermal resistance (Rtotal) of the wall is the sum of each layer's R factor:
Rtotal = Rdrywall + Rfiberglass + Rsiding
Given that:
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- Rdrywall = 0.56
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- Rfiberglass (calculated from thickness and material properties)
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- Rsiding = 2.6
With the inside temperature at 22 °C and the outside temperature at -2 °C, the temperature difference (ΔT) is 24°C. The wall surface area (A) is 3 m tall by 10 m wide, which gives 30 m2.
To find Q, we would plug the values into our formula.
For part (b), the presence of wood studs introduces a parallel path for heat flow. While the thermal resistance for the insulated parts remains the same, the studs have a different R value and cover a different proportion of the wall area. The effective R value for a section of the wall that includes a stud changes, and the overall Rtotal needs to be recalculated to account for a combination of the insulated sections and the stud sections. Since studs are on 16-inch centers, this dimension would be used to calculate the proportion of the wall covered by the studs compared to insulation.