Questions: ما هو مقدار سمك خليط من الخرسانة الذي له نفس مقدار العزل الحراري لحائط من الطوب الحراري سمكه 20 cm إذا علمت أن الموصلية الحرارية للخرسانة والطوب الحراري هي (0.8015 cal/cm · C) و (0.0022 cal/cm · C) على التوالي.

Solution Steps

We need to find the thickness of a concrete layer that provides the same thermal insulation as a 20 cm thick layer of firebrick. The thermal conductivities of concrete and firebrick are given as \(0.8015 \frac{\text{cal}}{\text{cm} \cdot \text{C}}\) and \(0.0022 \frac{\text{cal}}{\text{cm} \cdot \text{C}}\), respectively.

Thermal resistance \(R\) is given by: \[ R = \frac{L}{k} \] where \(L\) is the thickness of the material and \(k\) is the thermal conductivity.

To have the same thermal insulation, the thermal resistances of the concrete layer and the firebrick layer must be equal: \[ \frac{L_{\text{concrete}}}{k_{\text{concrete}}} = \frac{L_{\text{firebrick}}}{k_{\text{firebrick}}} \]

Given: \[ L_{\text{firebrick}} = 20 \, \text{cm} \] \[ k_{\text{concrete}} = 0.8015 \frac{\text{cal}}{\text{cm} \cdot \text{C}} \] \[ k_{\text{firebrick}} = 0.0022 \frac{\text{cal}}{\text{cm} \cdot \text{C}} \]

We solve for \(L_{\text{concrete}}\): \[ \frac{L_{\text{concrete}}}{0.8015} = \frac{20}{0.0022} \] \[ L_{\text{concrete}} = 20 \times \frac{0.8015}{0.0022} \] \[ L_{\text{concrete}} = 20 \times 364.3182 \] \[ L_{\text{concrete}} = 7286.364 \, \text{cm} \]

\[ L_{\text{concrete}} = 7286.364 \, \text{cm} \times 10 \, \frac{\text{mm}}{\text{cm}} \] \[ L_{\text{concrete}} = 72863.64 \, \text{mm} \]

The given options are:

• 263 mm
• 30 cm (300 mm)
• 301 mm
• 293.3 mm

Final Answer