Thermodynamics

A gas pushes on its container because its atoms keep hitting the walls, and pressure is the total perpendicular force from those collisions divided by the area. Temperature tracks the average kinetic energy of the atoms, $K_{\text{avg}} = \frac{3}{2}k_BT$, and the Maxwell–Boltzmann distribution shows how atom speeds spread out and shift higher when the gas gets hotter.

An ideal gas is a model where the atoms are tiny compared with the space they fill, move randomly, collide elastically and don't otherwise push on each other. Its pressure, volume, amount and temperature are linked by $PV = nRT = Nk_BT$, with T in kelvins, and extending a pressure–temperature graph down to zero pressure points to absolute zero.

When two systems at different temperatures are in thermal contact, energy flows on its own from the hotter one to the colder one by conduction, convection or radiation. Collisions pass energy from faster atoms to slower ones until both systems reach the same temperature, called thermal equilibrium, and no net energy flows.

The atoms of an ideal gas don't pull on each other, so its internal energy is just the total kinetic energy of its atoms: for an ideal monatomic gas $U = \frac{3}{2}nRT$, which changes only when the temperature does. The first law, $\Delta U = Q + W$, adds the energy from heating (Q) and the work done on the gas ($W = -P\Delta V$, positive when the gas is squeezed), and on a PV diagram the area under the curve gives the size of that work in isobaric, isovolumetric, isothermal and adiabatic processes.

Specific heat tells you how much energy it takes to warm 1 kg of a material by 1 K, so $Q = mc\Delta T$. Thermal conductivity sets how fast energy moves through a material by conduction: the rate $\frac{Q}{\Delta t} = \frac{kA\Delta T}{L}$ grows with the area and the temperature difference and shrinks as the material gets thicker.

Entropy describes how spread out a system's energy is, or how much of it is no longer available to do work. The second law says the total entropy of an isolated system never decreases, so energy spreads out on its own until the system reaches equilibrium; a closed system's entropy can drop only if energy leaves it. In AP Physics 2 this is qualitative only.