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AS & A-Level Physics 16 — Thermodynamics

AS & A-Level Physics 16 — Thermodynamics

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 16 of 26: Thermodynamics. Concepts, worked applications and misconception checks.

Physics EN A-Level
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Defining Internal Energy

Internal energy, UU, represents the total energy contained within a thermodynamic system due to the microscopic motion and interactions of its constituent particles (atoms or molecules). It is the sum of the random kinetic energies of all molecules, arising from their translational, rotational, and vibrational motions, and the random potential energies associated with the intermolecular forces between them. For an ideal gas, where intermolecular forces are negligible, the internal energy is solely the sum of the kinetic energies. In liquids and solids, where particles are closer and interact strongly, the potential energy contribution becomes significant, reflecting the energy stored in the bonds or forces holding the particles together. The internal energy is determined by the system's state, meaning its temperature, pressure, and volume.

Key points

  • Internal energy (UU) is the total microscopic energy of a system's molecules.
  • It comprises the sum of random molecular kinetic energy (due to motion) and potential energy (due to intermolecular forces).
  • For an ideal gas, UU is purely kinetic; for real gases, liquids, and solids, both kinetic and potential energies contribute.
  • Internal energy is a state function, meaning its value depends only on the current state of the system.

Worked example

Question

A pure crystalline solid is heated at its melting temperature at constant pressure until it melts. Explain why its internal energy increases even though its temperature remains constant.

Solution

1. Internal energy includes the random kinetic energy of the particles and the potential energy associated with their interactions.
2. A constant temperature means the average thermal kinetic energy does not increase during the phase change.
3. Energy supplied during melting increases the particles’ interaction potential energy as the ordered solid structure changes to a liquid. Energy accounting for a real process also includes any work done during expansion.

The rise in internal energy during melting is associated with increased intermolecular potential energy; the mean thermal kinetic energy stays constant while the temperature stays constant.

Common pitfalls

  • Confusing internal energy with macroscopic kinetic or potential energy: Internal energy refers to the microscopic energies within the system, not the energy of the system moving as a whole or its position in a gravitational field.
  • Assuming internal energy is only kinetic energy: While true for ideal gases, real substances have significant potential energy contributions from intermolecular forces, especially in liquids and solids, which changes during phase transitions even if temperature is constant.

Prerequisites

  • Basic understanding of energy forms.
  • Understanding of basic assumptions of kinetic theory, especially molecular motion.
  • Recall of kinetic energy formula and concept.
  • Recall of potential energy concept.
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