MinervaLab is a collection of interactive simulations of Thermodynamics and Statistical Physics developed in order to provide both teachers and students with a tool to visualize some specially difficult concepts related to this subjects.
Notebooks can be executed directly on Binder just by click on the file paths of the table below.
You can also access the main page here.
A Product Breakdown Structure (PBS) system has been used during the development of this proyect, assigning a unique code to every concept/program/element. The following chart can be useful as a guide to understand the names of the variables used along all the programs.
| PBS # | Concept | File path | Description |
|---|---|---|---|
| #110-000 | Van der Waals equation of state | apps/van_der_waals | A collection of programs aimed to visualize the different aspects of the phase transitions of a gas that follows the Van der Waals equation of state. |
| #111-000 | p(v, T) in 2D | apps/van_der_waals/p_v_2D.ipynb | A two-dimensional representation of the p(v,T) space during a gas-liquid phase transition (using reduced variables). |
| #112-000 | Change in volume | apps/van_der_waals/phase_transition_volume.ipynb | A visualization of how each phase volume changes during a phase transition. |
| #113-000 | Critical points | apps/van_der_waals/critical_points.ipynb | An interactive database of Van der Waals equation's a and b parameters that allows to visualize the critical points of a sort of elements. |
| #114-000 | Effect of a and b on the isotherms | apps/van_der_waals/effect_of_a_and_b.ipynb | A sort of representations of p(v,T) which gives the opportunity to interact with the a and b parameters in absolute variables. |
| #115-000 | Compare elements | apps/van_der_waals/compare_elements.ipynb | A program which allows to compare the p(v,T) isotherms for a given sort of elements. |
| #116-000 | p(v, T) in 3D | apps/van_der_waals/p_v_T_3D.ipynb | A three-dimensional representation of the p(v,T) space during a gas-liquid phase transition (using reduced variables). |
| #117-000 | Chemical potential | apps/van_der_waals/chemical_potential.ipynb | A program that allows to construct the chemical potential starting from the p(v,T) space. |
| #118-000 | Mathematical analysis | apps/van_der_waals/mathematical_analysis.ipynb | A visualization of Vander Waals' equation of state from a analytical point of view. |
| #119-000 | Effect of a and b on the function | apps/van_der_waals/parameters_analysis.ipynb | A visualization of Vander Waals' equation of state from a analytical point of view in order to study the effect of a and b parameters on the mathematical function. |
| #11A-000 | Non-existence zone | apps/van_der_waals/stability.ipynb | A visualization of dp/dv in order to study the stability of the system. |
| #11B-000 | Gibbs free energy | apps/van_der_waals/p_T_2D.ipynb | An interactive visualization of the p(T) plane and the Gibbs free energy for a gas-liquid phase transition. |
| #11C-000 | Effect of a and b on the isotherms (reduced variables) | apps/van_der_waals/effect_of_a_and_b_reduced.ipynb | A sort of representations of p(v,T) which gives the opportunity to interact with the a and b parameters in reduced variables. |
This software is licensed under the GNU General Public License v3.0. See the LICENSE file for details.
[1] Travis E. Oliphant. A guide to NumPy, USA: Trelgol Publishing, (2006).
[2] Stéfan van der Walt, S. Chris Colbert and Gaël Varoquaux. The NumPy Array: A Structure for Efficient Numerical Computation, Computing in Science & Engineering, 13, 22-30 (2011), DOI:10.1109/MCSE.2011.37 (publisher link)
[3] J. D. Hunter, Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering, vol. 9, no. 3, pp. 90-95, 2007
[4] Wes McKinney. Data Structures for Statistical Computing in Python, Proceedings of the 9th Python in Science Conference, 51-56 (2010) (publisher link)
Fernando Pérez and Brian E. Granger. IPython: A System for Interactive Scientific Computing, Computing in Science & Engineering, 9, 21-29 (2007), DOI:10.1109/MCSE.2007.53 (publisher link)