Revise Internal energy for Cambridge 9702 (16.1)

At its core, a substance's internal energy (U) is the grand total of all the chaotic kinetic and potential energies possessed by its individual particles (atoms or molecules). Imagine countless tiny particles jiggling, vibrating, and colliding randomly. Their movement contributes to kinetic energy, while the forces between them contribute to potential energy. It’s the sum of all these microscopic energies throughout the entire system.

The balance between kinetic and potential energy differs by state. In solids, particles vibrate in a fixed lattice, possessing both vibrational KE and significant PE from strong bonds. In liquids, particles have translational and vibrational KE, with PE from forces that are weaker than in solids but still significant. In gases, particles move freely with high KE, and the PE from intermolecular forces is negligible, especially in an ideal gas.

For the special case of an ideal gas, the model assumes there are no intermolecular forces between particles. This means the potential energy component of the internal energy is zero. Therefore, the internal energy of an ideal gas consists entirely of the sum of the random kinetic energies of its molecules. This leads to a crucial conclusion: the internal energy of a fixed mass of an ideal gas is directly proportional to its absolute temperature (in Kelvin).

$U \propto T$

For a monatomic ideal gas, this relationship can be expressed quantitatively as $U = \frac{3}{2}nRT$, where $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is the absolute temperature. This shows that if the temperature of an ideal gas is constant, its internal energy does not change.

The First Law of Thermodynamics is a cornerstone of physics, essentially a statement of the conservation of energy applied to thermodynamic systems. It explains how energy can be transferred into or out of a system, changing its internal energy, through two primary mechanisms: heating or doing work. The law provides a mathematical relationship between the change in internal energy ($\Delta U$), the heat added to the system ($Q$), and the work done on the system ($W$).

$\Delta U = Q + W$