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Thermodynamics FAQ

Which model accounts for the failure of the Dulong–Petit law at low temperature?

Einstein model (quantised oscillators). Einstein (1907) quantised each oscillator, explaining the decrease in specific heat at low T where oscillators freeze out due to ℏω ≫ k_BT.

Short Answer

Einstein model (quantised oscillators) is the best answer.

Thermodynamics questions usually test sign conventions, state variables, or what is being held constant. Before calculating, decide whether the system is exchanging heat, doing work, or both.

Einstein (1907) quantised each oscillator, explaining the decrease in specific heat at low T where oscillators freeze out due to ℏω ≫ k_BT.

Why This Answer Is Correct

This is a Hard-level question in Thermodynamics. The prompt is really testing whether you can connect the concept to its defining physical relationship instead of picking a nearby-but-wrong term.

Write the system boundary first. Many thermodynamics mistakes disappear once you know what counts as heat, work, and internal-energy change.

Choices At A Glance

  • A. Ideal gas model
  • B. Einstein model (quantised oscillators)
  • C. Ising model
  • D. Van der Waals model

When similar options appear on an exam, eliminate the ones that break the core law, use the wrong units, or confuse a definition with a consequence.

Topic Snapshot

Topic: Thermodynamics

Difficulty: Hard

Best next move: Re-state the governing law in your own words, then solve one more example from the same topic before moving on.