This question relates to Case Study 1. (Download the Data Sheet and Case Studies from the link in the quiz instructions.)

What is the magnitude of the conductive heat flow (in W) through the wall of the dome when it is 24°C inside and 6°C outside?

Select a single answer.

Question

This question relates to Case Study 1. (Download the Data Sheet and Case Studies from the link in the quiz instructions.)

What is the magnitude of the conductive heat flow (in W) through the wall of the dome when it is 24°C inside and 6°C outside?

Select a single answer.

BlackTom AI · Accepted Answer

Heat conduction through a uniform wall follows Fourier’s law in the form Q = k·A·ΔT / L (or equivalently Q = ΔT / R where R = L/(k·A)).

Relevant knowledge points:
- Steady-state conductive heat transfer through a planar (or locally planar) shell uses Q = kAΔT/L.
- R (thermal resistance) = L/(kA) in K/W; lower R means larger heat flow for a given ΔT.
- Use the dome geometry and material properties given in Case Study 1 (wall area A, thickness L, and thermal conductivity k).

Step-by-step calculation (using the Case Study 1 data):
1. From the case data: wall area A = 257.0 m^2, wall thickness L = 0.150 m, thermal conductivity k = 0.220 W/(m·K). Interior temperature Ti = 24 °C, exterior To = 6 °C so ΔT = Ti − To = 18 K.
2. Compute the conductive “k·A” product:
   k·A = 0.220 W/(m·K) × 257.0 m^2 = 56.54 W/K.
3. Compute the thermal resistance of the wall:
   R = L/(k·A) = 0.150 m / 56.54 W/K = 0.002653 K/W.
4. Compute the heat flow:
   Q = ΔT / R = 18 K / 0.002653 K/W = 6,786 W (rounded to the nearest whole watt).

Why this answer is correct:
- The calculation directly applies Fourier’s law with the Case Study’s provided A, L, and k. The intermediate steps (k·A, R, Q) show consistent units and arithmetic that yield Q = 6,786 W.

Why the other choices are incorrect:
- 13,566 W is roughly double the correct value (would imply either double area or half the resistance), which contradicts the given geometry/materials.
- 12,250 W and 18,855 W are likewise significantly larger and inconsistent with the provided A, L, k and ΔT.
- “None of the above” is incorrect because the computed value matches one of the choices.

Final confirmation: The computed conductive heat flow is 6,786 W, matching the provided correct answer (6786).

This question relates to Case Study 1. (Download the Data Sheet and Case Studies from the link in the quiz instructions.) What is the magnitude of the conductive heat flow (in W) through the wall of the dome when it is 24°C inside and 6°C outside? Select a single answer.单项选择题

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