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Understanding Thermodynamic Functions: Internal Energy, Enthalpy, Entropy, and Free Energy

This resource delves into the foundational concepts of thermodynamic functions in chemistry, focusing on internal energy (U), enthalpy (H), entropy (S), and free energy (G) as functions of temperature. Key principles such as the behavior of these functions at absolute zero and their variations at non-zero temperatures are explored. The text also covers contributions of heat, both at constant volume and pressure, and the implications of the third law of thermodynamics. This material is essential for anyone studying thermochemistry and statistical thermodynamics.

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Understanding Thermodynamic Functions: Internal Energy, Enthalpy, Entropy, and Free Energy

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  1. Chemistry 6440 / 7440 Thermochemistry

  2. Resources • McQuarrie, Statistical Thermodynamics, University Science Books, 1973 • Foresman and Frisch, Exploring Chemistry with Electronic Structure Methods, Chapter 4 • Cramer, Chapter 10 • Jensen, Chapter 12 • www.gaussian.com/thermo.html

  3. Thermodynamic Functions • U(T) - internal energy at absolute temperature T • H(T) = U(T) + PV = U(T) + RT - enthalpy • S(T) - entropy • G(T) = H(T) – T S(T) – free energy

  4. Thermodynamic Functions • at absolute zero, T = 0 U(0) = H(0) = G(0) U(0) = electronic energy + zero point energy S(0) = 0 for a pure crystalline substance (third law of thermodynamics)

  5. Thermodynamic Functions at T  0 • U(T) = U(0) + CvdT • heat at constant volume, molecule gains energy for translation (3/2 RT), rotation (3/2 RT) and vibration ( 1/(1-exp(-i/kT)) • H(T) = H(0) + CpdT • heat at constant pressure, molecule gains additional energy from expansion • S(T) > 0 • more states become accessible as the temperature increases

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