Summary

Summary

• Heat is energy transferred between bodies because of a temperature difference; temperature is the property that decides the direction of that transfer, measured on the Celsius, Fahrenheit, or (SI, absolute) Kelvin scale, related by $\dfrac{C}{5} = \dfrac{F-32}{9} = \dfrac{K-273}{5}$.
• Thermal expansion of solids is described by the coefficient of linear expansion $\alpha$ ($L = L_0(1+\alpha\,\Delta T)$), with $\beta = 2\alpha$ (areal) and $\gamma = 3\alpha$ (cubical) for an isotropic solid. Liquids and gases are described only by a cubical coefficient $\gamma$; a liquid's apparent expansion (observed in a container) is less than its real expansion by the container's own expansion. Gases follow Charles's law, $V_1/T_1 = V_2/T_2$ at constant pressure.
• Water's anomalous expansion: density is a maximum at $4\,^\circ\text{C}$, falling on both sides of it -- this is why a lake freezes at the surface first, leaving liquid water (near $4\,^\circ\text{C}$) beneath the ice, protecting aquatic life through winter.
• Specific heat capacity $c$ ($Q = mc\,\Delta T$) fixes how much heat a substance needs for a given temperature change; heat capacity is $mc$ for a particular body. Calorimetry's guiding principle is heat lost $=$ heat gained in an isolated system, the basis of the method of mixtures.
• A change of state absorbs or releases latent heat ($Q = mL$) at a fixed temperature; for a given substance the latent heat of vaporisation $L_v$ is much larger than the latent heat of fusion $L_f$.
• Heat travels by conduction ($Q/t = kA\,\Delta T/L$, needs a medium, no bulk motion), convection (bulk fluid motion, natural or forced), and radiation (electromagnetic waves, needs no medium).
• Kirchhoff's law links a surface's emissive power $e$ and absorptive power $a$ ($e/a$ is the same for every surface, equal to a black body's $e = 1$). Wien's displacement law ($\lambda_m T = b$) fixes how a black body's peak emission wavelength shifts with temperature; **Stefan's …