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Mathematics for Physics

231 Thermodynamics

A study of energy and its transformations that is used to predict the outcomes of physical, chemical, and biological processes.

The Zeroth Law. If each of two systems is in thermal equilibrium with a third system, those two systems share the same temperature. Thermal equilibrium means the systems can exchange energy and show no further change of temperature. This principle is used to treat temperature as a property of the present state and to decide whether heat will flow between systems.

The First Law. The internal energy of an isolated system stays constant. Internal energy is the total microscopic energy of the particles. An isolated system exchanges neither matter nor energy with its surroundings. Energy crosses a boundary as heat, transfer driven by a temperature difference, and as work, transfer through organized motion. This principle is used to balance energy for allowed changes.

The Second Law. In any real process the total entropy of an isolated system increases as energy disperses. Entropy measures how widely energy is spread among the microscopic motions available to the system. This principle is used to fix the natural direction of change and the limits on turning heat into useful work.

The Third Law. The entropy of a perfect crystal in internal equilibrium is zero at absolute zero of temperature. Absolute zero is the lowest temperature on the thermodynamic scale. This principle is used to set a fixed reference so absolute numerical entropies of substances can be assigned and tabulated.

The concept of state functions. Properties such as internal energy and entropy depend only on the present state of the system. A state is a complete set of macroscopic conditions that fix those properties. This principle is used to compute overall changes for irreversible processes by following any convenient path between the same start and end states.

231.1 References

  1. Levine, I. N. Physical Chemistry. Ch. 1 §1.3 — temperature and the Zeroth Law. Ch. 2 — the First Law; §2.10 — state functions. Ch. 3 — the Second Law. Ch. 5 §5.7 — conventional entropies and the Third Law.
  2. Atkins, P., de Paula, J., & Keeler, J. Atkins’ Physical Chemistry. Focus 2, Topic 2A — internal energy. Focus 3, Topic 3A — entropy; Topic 3C — measurement of entropy; Topic 3E — combining the First and Second Laws.