The Particulate Nature of Matter - Thermodynamics

The kinetic molecular theory states that matter is composed of small particles (atoms or molecules) in constant, random motion. The average kinetic energy of these particles is directly proportional to the absolute temperature of the substance in Kelvin ($T$).

Internal Energy ($U$) is defined as the sum of the total random kinetic energy and the total intermolecular potential energy of all the particles in a system. For an ideal gas, there are no intermolecular forces, so the internal energy consists only of kinetic energy.

Temperature must be used in Kelvin ($K$) for all thermodynamic calculations. The conversion is $T(K) = t(^{\circ}C) + 273.15$.

Specific Heat Capacity ($c$) is the amount of energy required to raise the temperature of $1\,kg$ of a substance by $1\,K$. During a temperature change, $Q = mc\Delta T$.

Specific Latent Heat ($L$) is the energy required to change the phase of $1\,kg$ of a substance at a constant temperature. $L_f$ is for fusion (melting/freezing) and $L_v$ is for vaporization (boiling/condensing). Formula: $Q = mL$.

An Ideal Gas is a theoretical gas that obeys the gas laws at all pressures, volumes, and temperatures. Assumptions include: particles are point masses, collisions are perfectly elastic, and there are no intermolecular forces.

The equation of state for an ideal gas is $PV = nRT$ or $PV = Nk_BT$, where $n$ is the number of moles and $N$ is the number of molecules.

The First Law of Thermodynamics is a statement of conservation of energy: $Q = \Delta U + W$, where $Q$ is heat added to the system, $\Delta U$ is the change in internal energy, and $W$ is the work done by the system.