A Hands-On Approach to Statistical Mechanics Lectures: Estimation of the Boltzmann Factor Through the Viscosity Experiment of a Falling Ball
DOI:
https://doi.org/10.26877/jp2f.v17i2.3577Keywords:
Boltzmann distribution, hands-on, stoke's viscosityAbstract
Statistical mechanics is the study of physics that relates macroscopic and microscopic parameters, often studied only with a theoretical approach, so it is relatively difficult to understand. For this reason, simple practical activities are needed to be connected with statistical mechanics, one of which is a viscosity experiment to determine the Boltzmann factor. This research was conducted to evaluate the viscosity value, coefficient of determination (R2), Reynolds number, activation energy and Boltzmann factor obtained from the experiment of dropping marbles in a tube containing cooking oil at a temperature variation of 303K-333K. Viscosity is calculated based on the observed terminal velocity of the ball using Stokes' Law. The magnitude of the activation energy is analyzed using the Arrhenius equation and the probability of fluid particles flowing was calculated using the Boltzmann factor. The results showed that the viscosity of cooking oil decreased with increasing temperature, with viscosity values ranging from 44-79 cP. The Reynolds number is evaluated in the range <2300 confirming laminar flow and suitable for Stokes' law. The activation energy of viscous flow was obtained as 11.489 kJ/mol with a coefficient of determination R² = 0.87712 which indicates a strong correlation between temperature and viscosity. The estimated number of moving particles based on the Boltzmann factor is evaluated to be 1.05% - 1.58%. This research validates that the hands-on approach can explain that the increase in kinetic energy of molecules at high temperatures reduces the viscosity of the fluid, thereby increasing the probability of fluid particles flowing.
References
[1] Koerfer E and Gregorcic B 2024 Exploring student reasoning in statistical mechanics: Identifying challenges in problem-solving groups Phys. Rev. Phys. Educ. Res. 20 010105
[2] Taufik M 2024 Enhancing Graphical Understanding of Statistical Distributions in Physics: Integrating Project-Based Learning with Desmos and Excel: A Case Study of Sixth-Semester Physics Education Students at FKIP Universitas Mataram 5
[3] Smith T I, Mountcastle D B and Thompson J R 2013 Identifying student difficulties with conflicting ideas in statistical mechanics AIP Conf. Proc. 1513 386–9
[4] Koerfer E 2025 Conceptual reasoning, intuition, and mathematics in physics: Statistical mechanics as a starting point for exploring student reasoning in upper-level university courses PhD Thesis Uppsala University
[5] Marshman E and Singh C 2015 Framework for understanding the patterns of student difficulties in quantum mechanics Phys. Rev. ST Phys. Educ. Res. 11 020119
[6] Smith T I, Mountcastle D B and Thompson J R 2015 Student understanding of the Boltzmann factor Phys. Rev. ST Phys. Educ. Res. 11 020123
[7] Baldovin M, Gradenigo G, Vulpiani A and Zanghì N 2025 On the foundations of statistical mechanics Phys. Rep. 1132 1–79
[8] Wen X, Dawod A Y and Yu X 2025 Comparing Instructional Models and Predicting Academic Performance in Physics Experiments: A Quasi-Experimental Study Intl. J. Learn. Teach. Edu. Res. 24 58–84
[9] Rathi M, Gupta P, Singh S, Singh S and Garg A 2025 Innovative STEM pedagogies for teaching trigonometric and mensuration concepts at secondary level Phys. Educ. 60
[10] Hernandez A et al 2021 Home experiments: a hands-on adaptation of the Experimental Physics II course at UFRJ for remote teaching Rev. Bras. Ensino Fis. 43 1–13
[11] George D J and Hammer N I 2015 Studying the binomial distribution using LabVIEW J. Chem. Educ. 92 389–94
[12] Cartier S F 2011 The statistical interpretation of classical thermodynamic heating and expansion processes J. Chem. Educ. 88 1531–7
[13] Zhang K 2020 Illustrating the Concepts of Entropy, Free Energy, and Thermodynamic Equilibrium with a Lattice Model J. Chem. Educ. 97 1903–7
[14] Posa M 2024 Volumetric Flask with White and Blue Balls: Demonstration of Microcanonical Ensemble of Small Populations J. Chem. Educ. 101 4057–63
[15] Bachtiar A, Aratri R P and Ermawati I R 2024 Penerapan Maxwell-Boltzman Pada Viskositas Berbasis Sensor Infrared Al-Irsyad J. Phys. Educ. 3
[16] Fazio C, Battaglia O R and Guastella I 2012 Two experiments to approach the Boltzmann factor: chemical reaction and viscous flow Eur. J. Phys. 33 359–71
[17] Shams M and Mirzaie M A 2025 Statistical Inference and Simulation for the Maxwell-Boltzmann Distribution Adv. Theory Simul. 8 2500148
[18] Janitra A A and Setiyawan T 2025 Analysis of Oil Viscosity Through Experimental Testing with a Stokes' Law-Based Prototype Phy. Sci. Edu. J. 5 99–109
[19] Brewer P G, Peltzer E T and Lage K 2021 Life at low Reynolds Number Re-visited: The apparent activation energy of viscous flow in sea water Deep Sea Res. I 176 103592
[20] Prasmono A S P and Atina Ahdika 2023 Analisis Regresi Berganda pada Faktor-Faktor yang Mempengaruhi Kinerja Fisik Preservasi Jalan dan Jembatan Di Provinsi Sumatera Selatan: Analisis Regresi Berganda ESDS 1 47–56
[21] Jalaluddin J, Akmal S, Za N and Ishak 2019 Analisa Profil Aliran Fluida Cair Dan Pressure Drop Pada Pipa L Menggunakan Metode Simulasi Computational Fluid Dynamic (CFD) J. Teknol. Kim. Unimal 8 97–108
[22] Tamburrino A and Niño Y 2025 The Universal Presence of the Reynolds Number Fluids 10 117
[23] Widyanto A, Rahmasari D and Hapsari S M 2024 Viscosity Analysis of Biodiesel Products Distributed Via Pipeline vol 6 (Padang, Indonesia: CV. Hei Publishing Indonesia)
[24] Widiyatun F, Selvia N and Dwitiyanti N 2019 Analisis Viskositas, Massa Jenis, dan Kekeruhan Minyak Goreng Curah Bekas Pakai STRING 4 25
[25] Ike E 2019 The study of viscosity-temperature dependence and activation energy for palm oil and soybean oil Glo. J. Pure Appl. Sci. 25 209–17
[26] Avramov I 2007 Viscosity activation energy Phys. Chem. Glasses 48
[27] Askur et al 2024 Teknik Kimia (Padang: CV Hei Publishing Indonesia)
[28] Fasina O O and Colley Z 2008 Viscosity and Specific Heat of Vegetable Oils as a Function of Temperature: 35°C to 180°C Int. J. Food Prop. 11 738–46
[29] Sahasrabudhe S N, Rodriguez-Martinez V, O'Meara M and Farkas B E 2017 Density, viscosity, and surface tension of five vegetable oils at elevated temperatures: Measurement and modeling Int. J. Food Prop. 20 1965–81
[30] Tan C P, Che Man Y B, Selamat J and Yusoff M S A 2001 Application of arrhenius kinetics to evaluate oxidative stability in vegetable oils by isothermal differential scanning calorimetry J. Am. Oil Chem. Soc. 78 1133–8
[31] Abdul-Hammed M, Adegboyega S A, Abdulwahab I and Jaji A O 2020 Viscosity-Temperature Stability, Chemical Characterization, and Fatty Acid Profiles of some Brands of Refined Vegetable Oil Phys. Chem. Res. 8 417–27
[32] Hernandez H 2017 Standard Maxwell-Boltzmann Distribution: Definition and Properties (doi:10.13140/RG.2.2.29888.74244)
[33] Hettema H 2012 The Unity of Chemistry and Physics: Absolute Reaction Rate Theory Hyle 18 145–73
