Heat conduction is a property of almost all solids and liquids. However, the thermal conductivity depends on physical and chemical boundary conditions.
Gases generally conduct heat poorly, which is why materials such as styrofoam* (a form of polystyrene), with its high proportion of air in the pores, are often used for insulation purposes.
For many solids, the rule applies: the better a substance conducts electric current, the greater its thermal conductivity. Metals therefore conduct heat very well, whereas most plastics have significantly lower thermal conductivity.
In liquids, the coupling between particles is weaker, which is why their ability to conduct heat is usually much lower than that of solids, though still higher than that of gases.
If one side of a body is heated and the other side cooled, heat flows from the hot side to the cold side. A stationary state then develops, resulting in a constant temperature gradient along the body. This can be compared to the voltage drop across an electrical resistor, which will be discussed in the next chapter.
The time required to reach this stationary state depends on both the thermal conductivity and the heat capacity of the body. These two quantities are therefore responsible for many thermodynamic properties of substances.
We now want to define thermal conductivity quantitatively, restricting ourselves to the stationary case.
By analogy to electrical current, one can define a heat power \(\dot{Q}\) (in watts), which specifies the amount of heat transferred per unit time between two heat reservoirs. The electrical voltage can, as mentioned above, be compared to the temperature difference, since this drives the heat flow.
Intuitively, one expects the heat flux to be proportional to the cross-sectional area of the body and inversely proportional to its length, since the greater the distance between the reservoirs, the smaller the conductivity.
From this, Fourier formulated in 1822 the law named after him, Fourier’s law:
$$
\dot{Q} = \lambda \frac{A}{d} \Delta T
$$
Here, \(\lambda\) is a material constant called the thermal conductivity, with units of \(\mathrm{W}/(\mathrm{m}\,\mathrm{K})\).
It explains, for example, why water feels significantly cooler than air at room temperature: water conducts heat away from the body much more efficiently. Tiles also feel colder than porous wooden floors at the same temperature because they conduct heat better.
Sometimes the thermal resistance \(R\) of a material is given, defined as the reciprocal of the thermal conductivity. The larger it is, the worse the material transports heat from one reservoir to another.
If two (identical or different) materials are joined together, the effective length of the body increases. Thus, the thermal resistances simply add up:
$$
R_\mathrm{total} = R_1 + R_2 + \dots + R_n
$$
If instead the thermal conductivities are used, the reciprocals must be added, and then the reciprocal of the result is taken.
Experiment: Heat conduction in solids
The different behavior of various materials in heat conduction can be demonstrated by placing blocks of identical size so that each is heated at one end at the same time. A match is attached to the opposite side of each block.
As soon as the heat reaches the respective match and the temperature is high enough, it ignites. The ignition time varies depending on the thermal conductivity of the material.