Thermodynamic Potentials - University Physics

The script begins by introducing thermodynamic potentials, which are key concepts in thermodynamics used in various processes. It mentions internal energy and enthalpy as examples, explaining their relevance in constant volume and constant pressure scenarios, respectively. The video also touches on the mathematical foundation needed to understand these potentials, specifically the concept of exact differentials. The presenter illustrates this with a function of two variables and explains partial differentiation, leading to the definition of exact differentials through the equality of cross-derivatives.

This paragraph delves deeper into the concept of exact differentials, emphasizing the condition for a differential to be exact: the equality of cross-derivatives. It uses a simple function to demonstrate this principle and connects it to thermodynamic potentials, which must be exact differentials. The paragraph then introduces the fundamental relation of thermodynamics, which is similar to the first law but uses exact differentials for heat and work, assuming quasi-static processes. This leads to the introduction of the concept of chemical potential, which accounts for changes in the number of particles in an open system.

The script explains chemical potential as a measure of the potential energy per particle related to its concentration gradient. It discusses how particles naturally move from regions of high to low chemical potential, spreading out to achieve uniform distribution. The chemical potential difference between two regions is related to the natural logarithm of their concentrations. The paragraph also introduces the thermodynamic definition of chemical potential as the derivative of internal energy with respect to the number of particles, while keeping entropy and volume constant.

The video script explores the differentials of enthalpy and internal energy, highlighting the natural variables associated with each thermodynamic potential. For enthalpy, it shows that the differential includes terms involving entropy and pressure, leading to the conclusion that entropy and pressure are its natural variables. The script also revisits the fundamental relation of thermodynamics, incorporating the chemical potential and its effect on the internal energy of an open system.

This section discusses Maxwell relations, which are derived from the exact differentials of thermodynamic potentials. It explains how these relations are useful for converting between different thermodynamic variables. The script provides an example of such a relation, showing how the derivative of temperature with respect to pressure at constant entropy is equal to the derivative of volume with respect to entropy at constant pressure.

The script introduces additional thermodynamic potentials: the Helmholtz free energy (F) and the Gibbs free energy (G). It explains the physical significance of these potentials, particularly the Helmholtz free energy, which represents the amount of energy available to do work. The Gibbs free energy is presented as a combination of enthalpy and internal energy, minus their product with temperature. The video also briefly mentions the grand potential, which is more relevant to open systems.

The final paragraph focuses on the Gibbs free energy and its role in determining the energetic favorability of chemical reactions. It explains that a negative change in Gibbs free energy (DG) indicates a favorable reaction, while a positive DG suggests a non-spontaneous process. The script concludes by summarizing the natural variables associated with each thermodynamic potential and their applications in thermodynamics.