Here's why:

* Thermal conductivity (k) is a material property. It describes how well a material conducts heat. It's inherent to the material itself and doesn't change with the thickness of the material.

* Thermal resistance (R) is what changes. It is a measure of how well a material resists heat flow. Thermal resistance is directly proportional to thickness and inversely proportional to thermal conductivity:

* R = thickness / k

Therefore, doubling the thickness of a wall doubles its thermal resistance, but doesn't affect its thermal conductivity.

In simpler terms:

* Think of thermal conductivity like how easily water flows through a pipe. A wide pipe (high conductivity) allows water to flow easily, while a narrow pipe (low conductivity) restricts flow. Doubling the length of the pipe doesn't change how wide it is, so the flow rate doesn't change (conductivity remains the same).

* Thermal resistance is like how much the pipe resists the flow of water. A longer pipe (greater thickness) offers more resistance to the flow of water, even if the pipe's width (conductivity) remains the same.

Important Note: While the thermal conductivity of the wall itself doesn't change, the rate of heat transfer through the wall will be halved because the thermal resistance is doubled.