7.1 Particles, Temperature, and Internal Energy

In solids, particles remain close to equilibrium positions and oscillate around them. Strong intermolecular forces keep average separation small and make solids resistant to compression. In liquids, particles remain close but can rearrange continuously, so liquids flow while still showing very low compressibility. In gases, average separation is much larger and intermolecular forces are usually negligible except during brief collisions.

This microscopic difference explains macroscopic density trends. Solids and liquids of the same substance usually have comparable densities, while gases are often orders of magnitude less dense under ordinary conditions. The point is not memorizing one ratio, but understanding why large average separation in gases implies large volume for the same amount of matter.

This proportionality is one of the central bridges in thermal physics: temperature is not a vague sensation of hotness, it is a measurable macroscopic variable linked to microscopic random motion. As T increases, average random molecular speed increases. As T decreases, average random motion decreases. The absolute minimum of kinetic energy implies an absolute temperature floor at 0 K.

Be careful with wording: temperature is related to average random kinetic energy, not total internal energy. Two bodies can share the same temperature but have very different total internal energy if their masses, particle counts, or intermolecular potential-energy contributions are different.

When two bodies in contact have different temperatures, energy transfers from the hotter body to the colder body. That transferred energy is thermal energy transfer (often called heat). Internal energy, in contrast, is the microscopic energy already stored in a body: random kinetic energy of particles plus potential energy associated with intermolecular configuration.

Thermal equilibrium is reached when there is no net thermal energy transfer between interacting bodies. In simple contact problems, this corresponds to equal final temperatures. Equilibrium does not require equal internal energies; it requires that the direction-driving temperature difference has vanished.

For calorimetry expressions with $\Delta T$, Celsius and Kelvin increments are interchangeable because one degree step is the same size in both scales. But laws with absolute $T$ itself, such as black-body radiation and kinetic-theory proportionalities, require Kelvin explicitly. Forgetting this conversion can generate impossible answers by factors of hundreds.

Interpretation guidance: hold temperature fixed and switch only phase first. You should see spacing and potential-energy depth change strongly while kinetic trend changes less dramatically. Then hold phase fixed and raise temperature; kinetic contributions rise, distribution shifts toward higher speeds, and compressibility trends become easier to explain microscopically.