A wall has cross-sectional area 11 m^2 and thickness .32 m. Its inside and outside temperatures are held constant at 150 Celsius and 14 Celsius.
Careful measurement indicates that the wall conducts thermal energy at the rate of 99.2 watts.
Conductivity is defined by the following statement: The rate at which thermal energy is conducted is equal to the product of the conductivity, the area of the wall, and the temperature gradient. The conductivity is thus equal to the rate of conduction divided by the area and the gradient.
The conductivity is thus
The rate of flow of thermal energy is proportional to c.s. area and to temperature gradient, with proportionality constant k.
This proportionality constant is called the thermal conductivity of the material. The proportionality for the average rate `dQ/ `dt at which thermal energy Q is conducted through a wall is thus
This makes sense because it ensures that all other things being equal, the rate at which thermal energy is transferred is proportional to the c.s. area of the wall and to the temperature gradient, as we might expect, as as we can confirm by experiment.
We conclude that
"thermal conductivity = k = (`dQ / `dt) / (A ( `dT / `dx) ) = rate of thermal energy flow / (c.s. area * temperature gradient).