Physics II / The Third Law and Low Temperatures
Practice question · Numerical answer

A crystal of carbon monoxide retains a residual entropy of kBln2k_B \ln 2 per molecule. For one mole, compute this in J/K, using R=8.314R = 8.314 J/mol/K, to one decimal place.

Hints
  1. Per mole, Boltzmann’s constant becomes the gas constant.
  2. Compute 8.314 x ln 2.
Show the answer

5.8 (answers within ±0.15 count)

Why

S=Rln2=8.314×0.693=5.8S = R\ln 2 = 8.314 \times 0.693 = 5.8 J/K per mole. The two nearly equivalent molecular orientations freeze in at random, so the crystal is not perfect and Planck’s statement does not apply.

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