Frank L. Lambert

Residual Entropy, the Third Law and Latent Heat

Abstract: A novel thermodynamic treatment of residual entropy in crystals, involving the configurational partition function, is suggested, which is consistent with both classical and statistical thermodynamics. It relates residual entropy to the inherent latent heat which would be released upon cooling if the reversible path were available. The nature of this heat is that if the crystal possessing residual entropy freezes above its Boltzmann’s characteristic temperature of molecular alignment, the difference in energy between different molecular arrangements is overcome by the kT heat bath to form a nearly-ideal solution. However, upon cooling below this characteristic temperature, they would separate with a concomitant release of the corresponding energy, provided the reversible path were available. Keywords: Configurational entropy, residual entropy, entropy of mixing, thermodynamics. 1. Introduction Residual entropy present in certain crystals comprised of non-symmetric molecules, e.g., CO, is detected only by the difference between spectroscopic calculations of the absolute entropy of gaseous CO and calorimetric measurements of heat capacity and phase change from 0 K to the temperature of the gas [1]. This phenomenon results in the occurrence of a non-zero entropy at absolute zero [2]. Residual entropy can be calculated by using the Boltzmann-Planck equation:

Coupling of Butyl Bromide on Hot Magnesium

A report of the formation of octane when butyl bromide is passed over magnesium turnings at high temperatures should be amended. Such coupling does take place over pure magnesium at more moderate temperatures but yields 3-methylheptane and sec-butyl bromide in addition to octane. Sec-butyl bromide itself forms no coupling product under such conditions but admixed with butyl bromide markedly increases the 3-methyl-heptane:octane ratio in the product.