Thermal Physics (AP Physics SuperCram Review)

When most objects heat up, they expand. The change in length (Delta L) can be calculated using a formula involving the initial length (L), the coefficient of thermal expansion (Alpha), and the change in temperature (Delta T). For two-dimensional objects, expansion occurs in all directions, including holes. Thermal conductivity describes how quickly heat flows through a substance, influenced by the material's coefficient of thermal conduction (K), surface area (A), temperature difference, and thickness. It is measured in Watts. Thermal conduction is one of three heat transfer methods, along with radiation and convection.

The ideal gas law is expressed as PV = nRT or PV = NkT, where n is the number of moles, R is the gas constant (8.31 J/mol·K), N is the number of molecules, and k is Boltzmann's constant (1.38 × 10^-23 J/K). Moles can be converted to molecules using Avogadro's number (6.02 × 10^23). When heat transfers between objects, Q gained equals Q lost. For temperature changes, use Q = mcΔT, and for phase changes, use Q = mL. Specific heat (c) indicates the energy needed to raise the temperature of 1 kg of a material by 1°C, while latent heat (L) pertains to phase changes. Calculations involve sequential heating and phase changes, ensuring energy conservation between interacting objects.

The root mean square (RMS) speed of gas molecules provides an average speed based on temperature (T in Kelvin) and the mass of a single gas molecule (m in kilograms). The mass of a molecule approximates the sum of protons and neutrons, converted to kilograms using atomic mass units (AMU). For gases with multiple atoms per molecule, adjustments are made. The average kinetic energy of a gas molecule is given by 1/2 mv^2, substituting v with RMS speed, resulting in 3/2 kT. There are four thermodynamic laws, starting with the zeroth law, which defines thermal equilibrium and underpins the concept of temperature.

Thermodynamic processes can be isothermal (constant temperature), adiabatic (no heat transfer), isochoric (constant volume), or isobaric (constant pressure). The first law of thermodynamics states ΔU = Q + W, where ΔU is the change in internal energy, Q is heat added, and W is work done on the gas. Work done can be visualized as the area under a PV diagram path, with sign conventions for expansion and compression. For monatomic gases, ΔU = 3/2 nRΔT. Heat (Q) is calculated from the first law, and cyclic processes have ΔU = 0. The second law of thermodynamics introduces entropy, indicating the universe's increasing disorder, and sets limits on heat engine efficiency.

Entropy, a measure of disorder, always increases in the universe. While localized entropy can decrease (e.g., water freezing), the total entropy of the system and surroundings increases. The second law also asserts that no heat engine can be 100% efficient due to inevitable heat loss. Efficiency is the ratio of work done to total heat input, influenced by temperature differences between heat source and sink. The Carnot engine represents the theoretical maximum efficiency, dependent on the temperatures of the heat source (Th) and sink (Tc), calculated as 1 - (Tc/Th). Practical applications require considering real-world irreversibilities and energy conservation principles.