A-Level Physics May/June 2024 Q3(b)(ii): a wire is stretched within its elastic limit at constant temperature.

1 answer

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  The internal energy of the wire is the sum of the total random kinetic energy and the total potential energy of its molecules.

  1. The problem states that the temperature of the wire is constant. The average kinetic energy of the molecules is directly proportional to the absolute temperature. Therefore, there is no change in the total kinetic energy of the molecules.

  2. When the wire is stretched, work is done on the wire to increase the average separation between its molecules. This work is done against the intermolecular forces of attraction. This increases the potential energy of the molecules.

  3. Since the internal energy is the sum of the kinetic and potential energies, and the kinetic energy is unchanged while the potential energy has increased, the overall internal energy of the wire increases.

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  How the marks are awarded

  • B1 — The first mark is awarded for correctly identifying that because the temperature is constant, there is no change in the kinetic energy of the molecules.
  • B1 — The second mark is awarded for explaining that stretching increases the separation of the molecules, which requires work to be done against intermolecular forces, thus increasing the potential energy of the molecules.
  • B1 — The final mark is for the concluding statement which correctly combines the previous two points: since potential energy increases and kinetic energy is unchanged, the total internal energy must increase.

  Common mistakes

  • Stating that internal energy is constant because temperature is constant, thereby ignoring the change in potential energy.
  • Incorrectly stating that potential energy decreases when the wire is stretched.
  • Confusing the concepts of heat and internal energy, for example by stating that because temperature is constant, no heat is transferred and therefore internal energy is constant.
  • Providing a vague answer, such as 'stretching adds energy', without specifying the types of energy (kinetic and potential) and how they are affected.

  Examiner tip: Always remember that internal energy is the sum of both the random kinetic and potential energies of molecules; a change in either will change the internal energy.

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