Thermal conductivity

The symbol is $k$, and on the AP Physics 2 sheet it lives in exactly one equation:

The left side is a rate in joules per second, which is a power in watts. Rearranging puts $k$ in $\mathrm{W/(m \cdot K)}$.

A large $k$ is not by itself a large rate. That is the error the equation exists to catch. Three other quantities sit in it.

• $A$ is the area of the face the energy crosses, the broad side of the slab.
• $L$ is the path length through the material, measured along the direction the energy travels: the thickness of a window, not its width.
• $\Delta T$ is the temperature difference between the two faces.

Every dependence is first order. Double $k$, $A$ or $\Delta T$ and the rate doubles; double $L$ and it halves. A thick slab of a good conductor can pass energy more slowly than a thin sheet of a poor one.

Essential knowledge 9.5.B.2 makes $k$ intrinsic: it depends on the arrangement and interactions of the atoms of the material, not on how much material there is. There is no sheet value for it, since it differs for glass and for copper; a question that needs one states it.

Watch the letter. The same sheet uses $k$ for the Coulomb constant, $9.0 \times 10^9\ \mathrm{N \cdot m^2/C^2}$, and for the spring constant, while $k_B$ is Boltzmann's constant. The Coulomb one is the trap, because it is the only $k$ with a number printed beside it.