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Register a new userMeasurement of the Boltzmann constant by Einstein. Problem of the 5-th Experimental Physics Olympiad. Sofia 9 December 2017
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Several consecutive experiments with specifically built set-up are described. Performing of the consecutive experimental tasks enables possibility to determine Boltzmanns constant $k_mathrm{_B}$. The fluctuations of the voltage $U(t)$ of series of capacitors connected in parallel with a constant resistance are measured. The voltage is amplified 1~million times $Y=10^6$. The amplified voltage $YU(t)$ is applied to a device, which give the voltage mean quared in time $U_2=left<(Y U(t))^2right>/U_0$. This voltage $U_2$ is measured with a multimeter. A series of measurements gives the possibility to determine the Boltzmanns constant from the equipartition theorem $Cleft<U^2 right>=k_mathrm{_B}T$. In order to determine the set-up constant $U_0$ a series of problems connected with Ohms law are given that are addressed to the senior students. For the junior high school students, the basic problem is to analyse the analog mean squaring. The students works are graded in four age groups S, M, L, XL. The last age group contains problems that are for university students (XL category) and include theoretical research of the set-up as an engineering device. This problem is given at the Fifth Experimental Physics Olympiad Day of the Electron, on December 2017 in Sofia, organized by the Sofia Branch of the Union of Physicists in Bulgaria with the cooperation of the Physics Faculty of Sofia University and the Society of Physicists of the Republic of Macedonia, Strumica.
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Several consecutive experiments are described with a printed circuit board PCB set-up, especially designed for these experiments. Doing the consecutive experimental tasks opens up possibility to determine the value of electron charge $q_e.$ The fluctuations of the voltage $U(t)$ should be measured for different illuminations of a photodiode. The voltage is amplified 1 million times $Y=10^6$. The amplified voltage $YU(t)$ is applied to the device, which gives the result of the value of the time averaged square of the voltage $U_mathrm{S}=left<(Y U(t))^2right>/U_0$. This voltage $U_mathrm{S}$ is measured with a multimeter. The series of measurements gives the possibility to determine the $q_e$ using the well known Schottky formula for the spectral density of the current noise $(I^2)_f=2q_eleft<Iright>.$ For the junior high school students, the basic problem is to analyze the analog squaring. Students work is separated and graded in four categories S, M, L, XL divided by age of students. For the last XL categories, the tasks contain problems oriented to physics university education program and include theoretical research of the PCB set-up as an engineering device. This is the problem of EPO6, December 2018 ``Day of the Charge considered. EPO6 is organized by Sofia branch of Union of physicists in Bulgaria in cooperation with Faculty of physics of Sofia University and Society of Physicists of Republic of Macedonia.
This is the problem of the 8$^mathrm{th}$ International Experimental Physics Olympiad (EPO). The task of the EPO8 is to determine Plank constant $hbar=h/2pi$ using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items -- they are instructive for physics education in general.Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best.
A simple experimental setup for measuring the Plancks constant, using Landauer quantization of the conductance between touching gold wires, is described. It consists of two gold wires with thickness of 0.5 mm and 1.5 cm length, and an operational amplifier. The setup costs less than $30 and can be realized in every teaching laboratory in two weeks. The usage of oscilloscope is required.
The classic brachistrochrone problem is standard material in intermediate mechanics. Many variations exist including some accessible to introductory students. While a quantitative solution isnt feasible in introductory classes, qualitative discussions can be very beneficial since kinematics, Newtons Laws, energy conservation and motion along curved trajectories all play a role. In this work, we describe an activity focusing on a qualitative understanding of the brachistochrone and examine the performance of freshmen, juniors and graduate students. The activity can be downloaded at https://w3.physics.arizona.edu/undergrad/teaching-resources .
We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.
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