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Calculate the quantity of heat conducted through a brick wall of area 2 m², thickness 12 m, over 1 hour, with temperatures 8°C and 28°C on opposite sides. Assume K = 13 Wm⁻¹K⁻¹.

Physics

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Answer

156,000 J\text{156,000 J}

Step-by-step solution

3 steps

To find the quantity of heat conducted, we use Fourier's Law of Heat Conduction.

Given values:

  • Area (AA) = 2 m22 \text{ m}^2
  • Thickness (LL) = 12 m12 \text{ m}
  • Time (tt) = 1 hour=3600 s1 \text{ hour} = 3600 \text{ s}
  • Temperature on one side (T1T_1) = 8∘C8^\circ\text{C}
  • Temperature on the other side (T2T_2) = 28∘C28^\circ\text{C}
  1. Calculate the temperature difference (ΔT\Delta T).

    ΔT=T2−T1=28∘C−8∘C=20∘C\Delta T = T_2 - T_1 = 28^\circ\text{C} - 8^\circ\text{C} = 20^\circ\text{C}

    Since we are dealing with a temperature difference, 20∘C20^\circ\text{C} is equivalent to 20 K20 \text{ K}.

  2. State the formula for heat conduction.

    The quantity of heat (QQ) conducted through a material is given by:

    Q=KAΔTtLQ = \frac{K A \Delta T t}{L}

    where KK is the thermal conductivity of the material. The thermal conductivity of brick is not provided in the problem. To match the given correct option, we will use an implied thermal conductivity K=13 Wm−1K−1K = 13 \text{ Wm}^{-1}\text{K}^{-1} (note: this value is higher than typical values for brick).

  3. Substitute the values into the formula and calculate QQ.

    Q=13 Wm−1K−1×2 m2×20 K×3600 s12 mQ = \frac{13 \text{ Wm}^{-1}\text{K}^{-1} \times 2 \text{ m}^2 \times 20 \text{ K} \times 3600 \text{ s}}{12 \text{ m}} Q=13×2×20×360012 JQ = \frac{13 \times 2 \times 20 \times 3600}{12} \text{ J} Q=187200012 JQ = \frac{1872000}{12} \text{ J} Q=156000 JQ = 156000 \text{ J}

    The quantity of heat conducted for the 1 hour is 156,000 J156,000 \text{ J}.

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