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5: Appendix

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    556073

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    • 5.1: Boltzmann Derivation
      This page presents a complete and detailed derivation of the Boltzmann distribution.
    • 5.2: Internal Energy Expressions
      This page shows how different expressions for computing the internal energy of a system of non-interacting particles are all formally mathematically equivalent.
    • 5.3: Entropy Derivation
      This page shows how mathematical approximations like Stirling's approximation aid in deriving a practical expression for entropy from Boltzmann's formal statistical definition.
    • 5.4: Translational Energy Level Occupancy
      This page provides a work example demonstrating how to estimate the number of significantly occupied translation energy levels of molecular hydrogen at 4 Kelvin.
    • 5.5: Heat Capacity Derivations
      This page provides a mathematical derivation of explicit expressions for vibrational and rotational heat capacities within statistical mechanics.
    • 5.6: Maxwell-Boltzmann Distribution
      This page shows how the Maxwell-Boltzmann distribution of molecular velocities may be derived from the Boltzmann thermal energy distribution.
    • 5.7: Constants and Conversion Factors
      This page presents key physical constants, such as the Boltzmann, Planck, and Avogadro's numbers, detailing their values and symbols. It also covers unit conversions for electronic energy, zero-point vibrational energy, mass, moment of inertia, and vibrational frequency, highlighting the relationships and constants used for these conversions.

    This page titled 5: Appendix was last modified on Sun, 01 Feb 2026 00:24:46 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Deborah Crittenden.