Which slab makes a better insulator if they have the same surface area but different thicknesses?

To determine which material serves as a better insulator, it's crucial to consider both thermal conductivity and thickness. The effectiveness of an insulating material is commonly assessed through its thermal resistance, often called R-value, which is calculated using the formula:

[ R = \frac{d}{k} ]

where ( d ) is the thickness of the material and ( k ) is the thermal conductivity (lower values of ( k ) indicate better insulating properties).

The choices present different materials with varying thermal conductivities and thicknesses.

• For the wood, it has a relatively low thermal conductivity (k=0.11) and a considerable thickness of 8 inches. This combination leads to a significant R-value.
• Concrete, while thick enough at 4 inches, has a much higher conductivity (k=1.0), resulting in lower insulation efficiency.
• Fiberglass has a very low thermal conductivity (k=0.042) but a minimal thickness of 2 inches, providing a decent R-value.
• Styrofoam also has a low thermal conductivity (k=0.029) and a thickness of 2 inches, which makes it a strong insulator as well.

Ultimately, the choice of wood with a thickness of