Derivation of Newton's law of cooling and heating: Heating the water then cooling it down naturally to the room temperature
Abstract
A simple experiment has been conducted to study Newton's law of cooling and heating by observing the nature of the increasing and decreasing water temperature by utilizing a data logger, a thermocouple, a pan, a hot plate, and water. The uncovered pan contained water which was subsequently heated on a hot plate. The water was heated at ambient temperature and normal atmospheric pressure to see that the temperature rose exponentially. Conversely, the temperature of hot water decreased exponentially when the heat source was switched off. The model for increasing and decreasing water temperature is following the Newton's law of cooling and heating. It was proven that the experimental data highly fit theoretical models. The temperature increment constant (ka) and the temperature decrement constant (kd) determined the rate of temperature changes. Low values of ka and kd led to the slow change in the temperature, either the increase or the decrease in the water temperature and vice versa. The ka > kd was observed for all given conditions so that the increasing rate in the water temperature was faster than its decrease. The result of this study can be applied as an example of contextual learning of physics for university students.
References
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Sokolowski, A. (2021). Unpacking structural domain of mathematics to aid inquiry in physics: a pilot study. Physics Education, 56(1), 015009. https://doi.org/10.1088/1361-6552/abc4db
Suryadi, A., Yuliati, L., & Wisodo, H. (2020). Students’ scientific reasoning on temperature and heat topic: A comparative study of students in urban and rural area. Momentum: Physics Education Journal, 4(1), 19–29. https://doi.org/10.21067/mpej.v4i1.4122
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Wibowo, E., Rokhmat, M., Sutisna, Yuliza, E., Khairurrijal, & Abdullah, M. (2016). The dynamics of a cylinder containing granules rolling down an inclined plane. In Powder Technology (Vol. 301). Elsevier B.V. https://doi.org/10.1016/j.powtec.2016.05.062
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Abdullah, M., Khairunnisa, S., & Akbar, F. (2014). Bending of sparklers. European Journal of Physics, 35(3), 1–11. https://doi.org/10.1088/0143-0807/35/3/035019
Aghayari, R., Maddah, H., Pourkiaei, S. M., Ahmadi, M. H., Chen, L., & Ghazvini, M. (2020). Theoretical and experimental studies of heat transfer in a double-pipe heat exchanger equipped with twisted tape and nanofluid. European Physical Journal Plus, 135(2). https://doi.org/10.1140/epjp/s13360-020-00252-8
Aleksandrov, A. A., Dzhuraeva, E. V., & Utenkov, V. F. (2013). Thermal conductivity of sodium chloride aqueous solutions. Thermal Engineering (English Translation of Teploenergetika), 60(3), 190–194. https://doi.org/10.1134/S0040601513030026
Aslani, H., & Moghiman, M. (2019). Experimental models to estimate supercooling behavior of ZrO2 nanofluid phase change materials. European Physical Journal Plus, 134(12). https://doi.org/10.1140/epjp/i2019-12969-2
Bastos, R. O., Cordeiro Filho, L. A., & Akio Ikeoka, R. (2022). Newton’s law of cooling with a low-cost thermoscope: physics in the time of covid-19. Physics Education, 57(4), 045001. https://doi.org/10.1088/1361-6552/ac5c6c
Bauer, C. F., & Chan, J. Y. K. (2019). Non-science majors learn about heat, temperature, and thermodynamics using the particulate nature of matter and guided-inquiry instruction. American Journal of Physics, 87(7), 550–557. https://doi.org/10.1119/1.5110500
Brody, J., & Brown, M. (2017). Transient heat conduction in a heat fin. American Journal of Physics, 85(8), 582–586. https://doi.org/10.1119/1.4983649
Chanthamanee, P., Jinda, P., Mani, M., & Prasitpong, S. (2022). Newton’s law of cooling experiment set using Arduino temperature sensor. Journal of Physics: Conference Series, 2145(1), 1–5. https://doi.org/10.1088/1742-6596/2145/1/012068
Christensen, J., Shah, N., Ortiz, N. A., Stroupe, D., & Reinholz, D. L. (2022). Tracking Inequity: An Actionable Approach to Addressing Inequities in Physics Classrooms. The Physics Teacher, 60(6), 414–418. https://doi.org/10.1119/5.0044392
Dale, D. A., Sutter, J., & Kloster, D. (2019). Asking Real-World Questions with Inquiry-Based Labs. The Physics Teacher, 57(8), 547–550. https://doi.org/10.1119/1.5131122
Dunnett, K., Gorman, M. N., & Bartlett, P. A. (2019). Assessing first-year undergraduate physics students’ laboratory practices: seeking to encourage research behaviours. European Journal of Physics, 40(1), 015702. https://doi.org/10.1088/1361-6404/aaf13b
Elmardi, O. M. (2017). Solutions to Problems in Heat Transfer. Transient Conduction Or Unsteady Conduction. Anchor Academic Publishing. https://books.google.co.id/books?id=aytiDgAAQBAJ
Fallahnezhad, N., & Reza Nazif, H. (2019). HeFallahnezhad, N., & Reza Nazif, H. (2019). Heat convection and hydrodynamic analysis of laminar developing nanofluid channel flow with variable properties under constant magnetic field and heat flux. European Physical Journal Plus, 134(8), 1–16. https:/. European Physical Journal Plus, 134(8), 1–16. https://doi.org/10.1140/epjp/i2019-12787-6
Foote, K., & Martino, S. (2018). Implementing Investigative Labs and Writing Intensive Reports in Large University Physics Courses. The Physics Teacher, 56(7), 466–469. https://doi.org/10.1119/1.5055331
Galeriu, C. (2018). An Arduino Investigation of Newton’s Law of Cooling. The Physics Teacher, 56(9), 618–620. https://doi.org/10.1119/1.5080580
Halliday, D., Resnick, R., & Walker, J. (2010). Fundamentals of Physics. John Wiley & Sons. https://books.google.co.id/books?id=y7lYHi4OZB0C
Jelicic, K., Geyer, M. A., Ivanjek, L., Klein, P., Kuchemann, S., Dahlkemper, M. N., & Susac, A. (2022). Lab courses for prospective physics teachers: what could we learn from the first COVID-19 lockdown? European Journal of Physics, 43(5). https://doi.org/10.1088/1361-6404/ac6ea1
Johal, R. S. (2023). The law of entropy increase for bodies in mutual thermal contact The law of entropy increase for bodies in mutual thermal contact. 79, 28–30. https://doi.org/10.1119/5.0124068
Kaufman, R., & Leff, H. (2022). Interdependence of the First and Second Laws of Thermodynamics. The Physics Teacher, 60(6), 501–503. https://doi.org/10.1119/5.0074493
Larsson, J., & Airey, J. (2021). On the periphery of university physics: Trainee physics teachers’ experiences of learning undergraduate physics. European Journal of Physics, 42(5). https://doi.org/10.1088/1361-6404/ac0e1e
May, J. M., De Grandi, C., Gerton, J. M., Barth-Cohen, L., Beehler, A., & Montoya, B. (2022). Bringing three-dimensional learning to undergraduate physics: Insight from an introductory physics laboratory course. American Journal of Physics, 90(6), 452–461. https://doi.org/10.1119/10.0009715
Meltzer, D. E. (2021). How Should Physics Teachers Be Prepared? A Review of Recommendations. The Physics Teacher, 59(7), 530–534. https://doi.org/10.1119/5.0022299
Nelson, H., Deyo, S., Granzier-Nakajima, S., Puente, P., Tully, K., & Webb, J. (2020). A mathematical model for meat cooking. European Physical Journal Plus, 135(3). https://doi.org/10.1140/epjp/s13360-020-00311-0
Onder, F., Şenyiǧit, Ç., & Silay. (2018). Effect of an inquiry-based learning method on students’ misconceptions about charging of conducting and insulating bodies. European Journal of Physics, 39(5). https://doi.org/10.1088/1361-6404/aac52a
Pacheco, M. G., Souza, R. de M. e, & Szilard, D. (2022). Multivalued specific heat. American Journal of Physics, 90(3), 187–193. https://doi.org/10.1119/10.0006899
Pols, F., Dekkers, P., & De Vries, M. (2019). Introducing argumentation in inquiry - A combination of five exemplary activities. Physics Education, 54(5). https://doi.org/10.1088/1361-6552/ab2ae5
Pols, F., Duynkerke, L., Van Arragon, J., Van Prooijen, K., Van Der Goot, L., & Bera, B. (2021). Students’ report on an open inquiry. Physics Education, 56(6), 1–5. https://doi.org/10.1088/1361-6552/ac27f8
Roll, M. F. (2020). Generalizing thermal resistance and a general thermal engine. American Journal of Physics, 88(10), 819–824. https://doi.org/10.1119/10.0001612
Silva, M. R., Martín-Ramos, P., & da Silva, P. P. (2018). Studying cooling curves with a smartphone. The Physics Teacher, 56(1), 53–55. https://doi.org/10.1119/1.5018696
Sokolowski, A. (2021). Unpacking structural domain of mathematics to aid inquiry in physics: a pilot study. Physics Education, 56(1), 015009. https://doi.org/10.1088/1361-6552/abc4db
Suryadi, A., Yuliati, L., & Wisodo, H. (2020). Students’ scientific reasoning on temperature and heat topic: A comparative study of students in urban and rural area. Momentum: Physics Education Journal, 4(1), 19–29. https://doi.org/10.21067/mpej.v4i1.4122
Vandervoort, K. (2020). Animal Size and Heat Transfer. The Physics Teacher, 58(2), 104–106. https://doi.org/10.1119/1.5144791
Vilarta Rodriguez, L., van der Veen, J. T., Anjewierden, A., van den Berg, E., & de Jong, T. (2020). Designing inquiry-based learning environments for quantum physics education in secondary schools. Physics Education, 55(6), 065026. https://doi.org/10.1088/1361-6552/abb346
Wagoner, K., Hynes, K. M., & Flanagan, D. (2018). Interesting Guided-Inquiry Labs for a Large-Enrollment, Active Learning Physics II Course. The Physics Teacher, 56(4), 244–247. https://doi.org/10.1119/1.5028243
Wang, L. R., Jin, Y. “Jenny,” & Wang, J. J. (2022). A simple and low-cost experimental method to determine the thermal diffusivity of various types of foods. American Journal of Physics, 90(8), 568–572. https://doi.org/10.1119/5.0087135
Wibowo, E., Rokhmat, M., Sutisna, Khairurrijal, & Abdullah, M. (2017). Reduction of seawater salinity by natural zeolite (Clinoptilolite): Adsorption isotherms, thermodynamics and kinetics. Desalination, 409, 146–156. https://doi.org/10.1016/j.desal.2017.01.026
Wibowo, E., Rokhmat, M., Sutisna, Yuliza, E., Khairurrijal, & Abdullah, M. (2016). The dynamics of a cylinder containing granules rolling down an inclined plane. In Powder Technology (Vol. 301). Elsevier B.V. https://doi.org/10.1016/j.powtec.2016.05.062
Will, J. B., Kruyt, N. P., & Venner, C. H. (2017). An experimental study of forced convective heat transfer from smooth, solid spheres. International Journal of Heat and Mass Transfer, 109, 1059–1067. https://doi.org/10.1016/j.ijheatmasstransfer.2017.02.018
Authors
Wibowo, E., Ulya, N., Farizi, M. R., & Fitriyanti, N. (2023). Derivation of Newton’s law of cooling and heating: Heating the water then cooling it down naturally to the room temperature. Momentum: Physics Education Journal, 7(1), 78–92. https://doi.org/10.21067/mpej.v7i1.6889
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