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- https://chem.libretexts.org/Courses/Grinnell_College/CHM_363%3A_Physical_Chemistry_1_(Grinnell_College)/16%3A_Math_Chapters/16.03%3A_Partial_DifferentiationThe development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.
- https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.04%3A_Exact_and_Inexact_Differentials/10.4.02%3A_Exact_and_Inexact_DifferentialsIf you are given a function of more than one variable, you can calculate its total differential using the definition of a total differential of a function \(u\): (\(du=\left(\frac{\partial u}{\partial...If you are given a function of more than one variable, you can calculate its total differential using the definition of a total differential of a function \(u\): (\(du=\left(\frac{\partial u}{\partial x_1} \right)_{x_2...x_n} dx_1+\left( \frac{\partial u}{\partial x_2} \right)_{x_1, x_3...x_n} dx_2+...+\left( \frac{\partial u}{\partial x_n} \right)_{x_1...x_{n-1}} dx_n\)).
- https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.04%3A_Exact_and_Inexact_Differentials/10.4.06%3A_Exact_and_Inexact_Differentials_(Summary)If the derivatives are identical, we conclude that the differential \(df\) is exact, and therefore it is the total differential of a function \(f(x,y)\). It is important to keep in mind that the integ...If the derivatives are identical, we conclude that the differential \(df\) is exact, and therefore it is the total differential of a function \(f(x,y)\). It is important to keep in mind that the integration constant in the first case will be an arbitrary function of \(y\), and in the second case an arbitrary function of \(x\). This means that the integral of \(df\) along any path is simply the function \(f\) evaluated at the final state minus the function \(f\) evaluated at the initial state:
- https://chem.libretexts.org/Courses/DePaul_University/Physical_Chemistry_for_Biological_Sciences/11%3A_Entropy_and_The_Second_Law_of_Thermodynamics/11.02%3A_Nonequilibrium_Isolated_Systems_Evolve_in_a_Direction_That_Increases_Their_Energy_DispersalAn isolated system, one that does not exchange heat with its surroundings, not at equilibrium will evolve in a direction that increases the overall energy dispersion of the state. The system will reac...An isolated system, one that does not exchange heat with its surroundings, not at equilibrium will evolve in a direction that increases the overall energy dispersion of the state. The system will reach equilibrium when the energy dispersal, or entropy (\(S\)), is maximum.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Mathematical_Methods_in_Chemistry_(Levitus)/09%3A_Exact_and_Inexact_DifferentialsUnderstand the concept of exact and inexact differentials. Be able to test whether a differential is exact or not. Understand the role of exact and inexact differentials in thermodynamics. Thumbnail: ...Understand the concept of exact and inexact differentials. Be able to test whether a differential is exact or not. Understand the role of exact and inexact differentials in thermodynamics. Thumbnail: These are just three of the infinitely many paths between a state at point A at some time to point B at some other time. A discussion of exact and inexact differentials is strongly connected to understanding the differences between paths and states (CC BY-SA 3.0; Matt McIrvin via Wikipedia)
- https://chem.libretexts.org/Courses/Grinnell_College/CHM_364%3A_Physical_Chemistry_2_(Grinnell_College)/14%3A_Math_Chapters/14.08%3A_Partial_DifferentiationThe development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.
- https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_110A%3A_Physical_Chemistry__I/UCD_Chem_110A%3A_Physical_Chemistry_I_(Koski)/Text/10%3A_MathChapters/10.08%3A_Partial_DifferentiationThe development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Mathematical_Methods_in_Chemistry_(Levitus)/09%3A_Exact_and_Inexact_Differentials/9.02%3A_Exact_and_Inexact_DifferentialsIf you are given a function of more than one variable, you can calculate its total differential using the definition of a total differential of a function \(u\): (\(du=\left(\frac{\partial u}{\partial...If you are given a function of more than one variable, you can calculate its total differential using the definition of a total differential of a function \(u\): (\(du=\left(\frac{\partial u}{\partial x_1} \right)_{x_2...x_n} dx_1+\left( \frac{\partial u}{\partial x_2} \right)_{x_1, x_3...x_n} dx_2+...+\left( \frac{\partial u}{\partial x_n} \right)_{x_1...x_{n-1}} dx_n\)).
- https://chem.libretexts.org/Courses/Knox_College/Chem_321%3A_Physical_Chemistry_I/13%3A_MathChapters/13.08%3A_H-_Partial_DifferentiationThe development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.
- https://chem.libretexts.org/Courses/Knox_College/Chem_322%3A_Physical_Chemisty_II/16%3A_MathChapters/16.08%3A_Partial_DifferentiationThe development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Chemical_Thermodynamics_(Supplement_to_Shepherd_et_al.)/09%3A_Fundamental_7_-_Variable_Changes/9.01%3A_Partial_DifferentiationThe development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.
