The Particulate Nature of Matter

Internal energy $U$ is the total kinetic and potential energy of every particle in a system — it is not the same thing as temperature (the average random KE per particle) or thermal energy transferred. The first law, $\Delta U = Q + W$, is just conservation of energy applied to a gas, but IB defines $W$ as the work done ON the gas: compressing a gas gives $W>0$, letting it expand and push a piston gives $W<0$. Getting this backwards is the single most common way to lose marks in this section.

For an ideal gas, internal energy depends ONLY on temperature — nothing else. So whenever a process is described as isothermal, $\Delta U = 0$ is guaranteed, no matter what Q and W turn out to be. Students who reflexively reach for $\Delta U = Q+W$ and go hunting for a value of Q often fall straight into a wrong-answer trap that the isothermal condition was designed to avoid.

Entropy $S$ measures the number of microscopic arrangements consistent with a system's macroscopic state, and for a reversible process at constant temperature, $\Delta S = Q/T$. Heat engines convert thermal energy from a hot reservoir into useful work while rejecting the rest to a cold reservoir, giving efficiency $\eta = W/Q_H = 1 - Q_C/Q_H$. No real engine beats the Carnot ceiling, $\eta_{Carnot} = 1 - T_C/T_H$, which strictly requires temperatures in kelvin.

Thermal energy always moves spontaneously from hot to cold, but the route depends on what's available: conduction is particle-to-particle collision (dominant in solids, especially metals with free electrons), convection needs a fluid that can develop density differences and circulate, and radiation is the only mechanism that works through a vacuum — it's how the Sun's energy reaches Earth at all. Specific heat capacity ($Q=mc\Delta T$) and specific latent heat ($Q=mL$) describe the energy involved without saying which mechanism delivered it.

A black body absorbs all incident radiation and emits the maximum possible for its temperature; emissivity $e$ scales a real surface's output relative to that ideal. Total radiated power follows the Stefan-Boltzmann law, $P = e\sigma A T^4$, while Wien's law, $\lambda_{max}T = 2.90\times10^{-3}\ \text{m K}$, links peak emitted wavelength to absolute temperature. Both formulas demand kelvin, and for a sphere like a star, the radiating surface area is $4\pi r^2$, not a flat disc.