Heat Conduction

Heat conduction is a property of almost all solids and liquids. However, the thermal conductivity depends on physical and chemical boundary conditions. Gases are generally poor conductors of heat, which is why polystyrene, for example, which is a form of polystyrene, is often used for insulation purposes due to the high proportion of air in the pores. The following applies to many solid bodies: the better a substance conducts electricity, the greater its thermal conductivity. Metals conduct heat very well, whereas most plastics have a significantly lower thermal conductivity. In liquids, the coupling of the particles to one another is lower, which is why the ability to conduct heat is usually significantly lower than in solids, but still more significant than that of gases.

When you heat one side of a body and cool another side, the heat spreads from the hot side to the cold side. A stationary state then develops, which results in a constant temperature gradient along the body. This can be roughly compared to the voltage drop across an electrical resistor, which will be discussed in the next chapter. The time it takes to reach this steady-state depends on the thermal conductivity and the heat capacity of the body. These two quantities are therefore responsible for many of the thermodynamic properties of materials. The concept of thermal conductivity is now to be recorded quantitatively in the following, whereby we want to limit ourselves to the stationary state.

In analogy to the electrical current, a heat output $\dot{Q}$ can be specified with the unit watt, which indicates the amount of heat transferred between two heat reservoirs per unit of time. As already mentioned, the electrical voltage can then be equated with the temperature difference, since this is responsible for the flow of heat. Intuitively, one expects the heat flow to increase proportionally to the area of ​​the body. At the same time, it should be inversely proportional to the length of the body, since the further apart the reservoirs are, the smaller the thermal conductivity. In 1822, Fourier formulated the Fourier law, which was named after him: \begin{equation} \boxed{\dot{Q} = \lambda \frac{A}{d} \Delta T} \end{equation} The variable $\lambda$ is a material constant and is called thermal conductivity. Its unit is therefore $1\,\mathrm{W}/(\mathrm{m}\,\mathrm{K})$. For example, it is responsible for the fact that water at room temperature appears significantly cooler than air because water dissipates heat from the body much better. Tiles also feel much colder at the same temperature as porous wood floors because they conduct heat well.

Sometimes the thermal resistance $R$ of a substance is also given, which is defined as the reciprocal of the thermal conductivity. The larger this is, the worse a substance transports heat from one reservoir to another. When two (same or different) fabrics are strung together, the length of the body effectively increases. From this it follows that the thermal resistances $R$ can simply be added up: \begin{equation} R_\mathrm{total} = R_1 + R_2 + \dots + R_n \end{equation} If the thermal conductivity is used instead, the reciprocal values ​​must be added and the reciprocal value formed from the resulting number.