The prevailing beliefs in the scientific and engineering literature are that: (i) thermodynamics is explained and justified by statistical mechanics: (ii) entropy is a statistical measure of disorder; and (iii) for given values of energy, volume, and amounts of constituents, the largest value of entropy corresponds to both a thermodynamic equilibrium state and the ultimate disorder. In this paper, we provide: (i) a summary of the beliefs as stated by some eminent scientists; (ii) experimental evidence that casts serious doubt about the validity of the beliefs; (iii) an outline of a nonstatistical unified quantum theory of mechanics and thermodynamics; (iv) an outline of a nonquantal, nonstatistical exposition of thermodynamics, valid for all systems (both macroscopic and microscopic), and for all states (both thermodynamic equilibrium and not thermodynamic equilibrium); (v) the definition and analytical expression of the entropy of thermodynamics: (vi) the interpretation of entropy as both a measure of the quantum-theoretic spatial shape of a molecule, and an indicator of order: and (vii) nonstatistical answers to the questions that motivated the introduction os statistical mechanics.