Definition: Conduction

The rate of heat transfer within a substance with thermal conductivity coefficient $k$ is $$\frac{dQ}{dt}=kA\frac{dT}{dx}$$

Theorem: Analogy to circuits

An analogy can be made between heat transfer and electric circuits, with the equivalences $$\frac{dQ}{dt}\equiv I\qquad k\equiv \sigma\qquad \frac{dT}{dx}\equiv\frac{dV}{dx}= E$$

Definition: Radiation

The Stefan-Boltzmann law states that the radiation power per unit area of a blackbody at temperature $T$ is $$\frac{P}{A}=\sigma T^4$$ where $\sigma = 5.67 \times 10^{-8} \,\unit{W\cdot m^{-2}\cdot K^{-4}}$ is the Stefan-Boltzmann constant. A blackbody absorbs all incident radiation. The emissivity $\epsilon<1$ describes the ratio between the radiation emitted/absorbed by a graybody and the radiation emitted/absorbed by a blackbody at the same temperature.

Definition: Latent heat

The latent heat $L$ of an object is the heat required in a phase transition of the object. $$Q=mL$$

Theorem: Evaporation and boiling

The processes of evaporation and condensation are the transfers of certain molecules from the liquid to gas state and vice versa. To this end we define two quantities:

• The saturated pressure of a gas is the pressure at which the evaporation and condensation rates are equal. The saturated pressure is a function of temperature.
• The relative humidity of the gas is the ratio of the existing pressure $p$ to the saturated pressure at that temperature: $r=p/p_s$. When the relative humidity is less than 1, then the liquid evaporates faster than it condenses. If the relative humidity is greater than 1, then the liquid condenses faster than it evaporates.

A gas will boil when the saturated vapor pressure is able to form bubbles, i.e. when the saturated vapor pressure is greater than the atmospheric pressure.

Definition: Surface tension

Surface tension arises from attractive electrostatic forces between molecules of a liquid. The force and potential energy due to surface tension are $$F=\sigma \ell\qquad U=\sigma A$$