8. Consider a cubical building with sides of length 7 m. The walls are made of concrete with a thickness of 0.25 m and thermal conductivity of 0.8 W /m · °C. The temperature outside is Tout = -5 °C, while the temperature inside is Tin = 20 °C. How much energy (in joules) must the heating system provide in 12 hours to maintain the inside temperature constant? Assume heat cannot escape through the floor. In other words, assume that heat escapes through only five sides of the cube. Show your work.

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**Problem 8: Heat Transfer in a Cubical Building**

*Scenario:*

Consider a cubical building with sides of length \( 7 \, \text{m} \). The walls are composed of concrete with a thickness of \( 0.25 \, \text{m} \) and possess a thermal conductivity of \( 0.8 \, \text{W/m} \cdot \degree \text{C} \). The exterior temperature is \( T_{\text{out}} = -5 \degree \text{C} \), while the interior temperature is \( T_{\text{in}} = 20 \degree \text{C} \).

*Task:*

Determine the amount of energy (in joules) that the heating system must supply over a 12-hour period to maintain a constant inside temperature. Assume that heat loss occurs only through the five sides of the cube, excluding the floor.

*Instructions:*

Show your calculations and reasoning.

*Key Concepts Involved:*

- **Heat Transfer Calculation**: Use the formula for heat conduction.
- **Thermal Conductivity**: Understand how this property affects heat transfer.
- **Real-world Application**: Consider this a practical exercise in energy management for buildings.

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No graphs or diagrams accompany this problem, but visualizing the cube and temperature gradients can help in understanding the context.
Transcribed Image Text:Sure! Here’s a transcription of the text with an educational focus: --- **Problem 8: Heat Transfer in a Cubical Building** *Scenario:* Consider a cubical building with sides of length \( 7 \, \text{m} \). The walls are composed of concrete with a thickness of \( 0.25 \, \text{m} \) and possess a thermal conductivity of \( 0.8 \, \text{W/m} \cdot \degree \text{C} \). The exterior temperature is \( T_{\text{out}} = -5 \degree \text{C} \), while the interior temperature is \( T_{\text{in}} = 20 \degree \text{C} \). *Task:* Determine the amount of energy (in joules) that the heating system must supply over a 12-hour period to maintain a constant inside temperature. Assume that heat loss occurs only through the five sides of the cube, excluding the floor. *Instructions:* Show your calculations and reasoning. *Key Concepts Involved:* - **Heat Transfer Calculation**: Use the formula for heat conduction. - **Thermal Conductivity**: Understand how this property affects heat transfer. - **Real-world Application**: Consider this a practical exercise in energy management for buildings. --- No graphs or diagrams accompany this problem, but visualizing the cube and temperature gradients can help in understanding the context.
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