Съдържание

IOM 2019, Експеримент — Задача 2. Exercise 1.2: Measuring the expansion coefficient of plastic tube

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Всички материали от IOM 2019

The 4th International Olympiad of Metropolises — Carbon Dioxide Solubility in Water

Recommendations Regarding the Experiment

There are two long exercises in the proposed experiment. Exercise 1.5 and exercise 2.1 in total may take more than three hours to complete. Consider this fact when allocating time and responsibilities to the participants during the experiment.

Условие

Use a 20-ml syringe to measure the inner volume $v_0$ of the tube. Also measure the length $L$ of the tube. Calculate the cross-section area $s_0$ of the tube channel.

If additional pressure is created inside the plastic tube then the cross-section area of the tube channel changes. Suggest a method to reliably measure the relative change in cross-section area $\Delta s / s_0$ as a function of additional pressure $\Delta p$ in the tube. Explain the proposed method with the help of drawings similar to those shown in Fig. 1; make annotations to all the elements in your drawings. Measure the above relationship by obtaining at least 7 experimental points in the whole possible range of positive additional pressures in the tube. Draw a graph of the relationship obtained. Determine the slope of the graph.

Отговори

Решение

Exercise 1.2

Volume of the tube channel $v_0$ : 11 ml

Tube length $L$ : 149 cm

Cross-section area of the tube channel $s_0$ : 7.4 mm $^2$

$\Delta p$ , mmHg	$x_1$ , cm	$x_2$ , cm	$\dfrac{\Delta s}{s_0}$ , cm
5.8	0.5	89.9	0.0000
20.7	2	91.2	0.0022
41.4	4	93.1	0.0034
63.7	6	95	0.0045
87.6	8	96.85	0.0062
111.8	10	98.7	0.0078
138.4	12	100.5	0.0101
165	14	102.3	0.0123
194.4	16	104	0.0157
224.3	18	105.7	0.0190
256.4	20	107.5	0.0213

Explain the method of measuring the relationship between the tube cross-section area and pressure in the tube.

Five stages separated by dashed lines: the tube along a measuring tape is filled with water from a container by a syringe; the water column of length x0 is measured with the manometer at 00.0; after pressing the syringe the manometer shows 12.3 and the water column has length x.

\frac{\Delta s}{s_0} = 1 - \frac{x}{x_0}

Slope of the graph: 8.3 mmHg $^{-1}$

Graph of $\dfrac{\Delta s}{s_0}$ against $\Delta p$

Graph of Δs/s0 (0.000 to 0.025) against Δp (0 to 300) with measured points and a straight fitted line; error bars at the second and the last point.

Оригинал в Архива: phys-task-prak-iom-2019-en.pdf · официални решения: phys-solution-prak-iom-2019-en.pdf