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IPhO 1967, Теория и експеримент — Experimental problem

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Problems of the 1st International Physics Olympiad (Warsaw, 1967)

Source history and reconstruction

Problems of the 1st International Physics Olympiad1

(Warsaw, 1967)

Waldemar Gorzkowski

Institute of Physics, Polish Academy of Sciences, Warsaw, Poland2

Abstract

The article contains the competition problems given at he 1st International Physics Olympiad (Warsaw, 1967) and their solutions. Additionally it contains comments of historical character.

Introduction

One of the most important points when preparing the students to the International Physics Olympiads is solving and analysis of the competition problems given in the past. Unfortunately, it is very difficult to find appropriate materials. The proceedings of the subsequent Olympiads are published starting from the XV IPhO in Sigtuna (Sweden, 1984). It is true that some of very old problems were published (not always in English) in different books or articles, but they are practically unavailable. Moreover, sometimes they are more or less substantially changed.

The original English versions of the problems of the 1st IPhO have not been conserved. The permanent Secretariat of the IPhOs was created in 1983. Until this year the Olympic materials were collected by different persons in their private archives. These archives as a rule were of amateur character and practically no one of them was complete. This article is based on the books by R. Kunfalvi [1], Tadeusz Pniewski [2] and Waldemar Gorzkowski [3]. Tadeusz Pniewski was one of the members of the Organizing Committee of the Polish Physics Olympiad when the 1st IPhO took place, while R. Kunfalvi was one of the members of the International Board at the 1st IPhO. For that it seems that credibility of these materials is very high. The differences between versions presented by R. Kunfalvi and T. Pniewski are rather very small (although the book by Pniewski is richer, especially with respect to the solution to the experimental problem).

As regards the competition problems given in Sigtuna (1984) or later, they are available, in principle, in appropriate proceedings. “In principle” as the proceedings usually were published in a small number of copies, not enough to satisfy present needs of people interested in our competition. It is true that every year the organizers provide the permanent Secretariat with a number of copies of the proceedings for free dissemination. But the needs are continually growing up and we have disseminated practically all what we had.

The competition problems were commonly available (at least for some time) just only from the XXVI IPhO in Canberra (Australia) as from that time the organizers started putting the problems on their home pages. The Olympic home page www.jyu.fi/ipho contains the problems starting from the XXVIII IPhO in Sudbury (Canada). Unfortunately, the problems given in Canberra (XXVI IPhO) and in Oslo (XXVII IPhO) are not present there.

The net result is such that finding the competition problems of the Olympiads organized prior to Sudbury is very difficult. It seems that the best way of improving the situation is publishing the competition problems of the older Olympiads in our journal. The

1 This is somewhat extended version of the article sent for publication in Physics Competitions in July 2003. 2 e-mail: gorzk@ifpan.edu.pl

question arises, however, who should do it. According to the Statutes the problems are created by the local organizing committees. It is true that the texts are improved and accepted by the International Board, but always the organizers bear the main responsibility for the topics of the problems, their structure and quality. On the other hand, the glory resulting of high level problems goes to them. For the above it is absolutely clear to me that they should have an absolute priority with respect to any form of publication. So, the best way would be to publish the problems of the older Olympiads by representatives of the organizers from different countries.

Poland organized the IPhOs for thee times: I IPhO (1967), VII IPhO (1974) and XX IPhO (1989). So, I have decided to give a good example and present the competition problems of these Olympiads in three subsequent articles. At the same time I ask our Colleagues and Friends from other countries for doing the same with respect to the Olympiads organized in their countries prior to the XXVIII IPhO (Sudbury).

I IPhO (Warsaw 1967)

The problems were created by the Organizing Committee. At present we are not able to recover the names of the authors of the problems.

Editorial source note: this is Waldemar Gorzkowski’s extended 2003 historical reconstruction, including worked solutions. It explicitly states that the original English versions were not conserved. The five tasks below preserve this edition; they are not presented as surviving original 1967 English sheets.

Условие

The following devices and materials are given:

Balance (without weights)
Calorimeter
Thermometer
Source of voltage
Switches
Wires
Electric heater
Stop-watch
Beakers
Water
Petroleum
Sand (for balancing)

Determine specific heat of petroleum. The specific heat of water is 1 cal/(g·°C). The specific heat of the calorimeter is 0.092 cal/(g·°C).

Discuss assumptions made in the solution.

Решение

The devices given to the students allowed using several methods. The students used the following three methods:

Comparison of velocity of warming up water and petroleum;
Comparison of cooling down water and petroleum;
Traditional heat balance.

As no weights were given, the students had to use the sand to find portions of petroleum and water with masses equal to the mass of calorimeter.

First method: comparison of velocity of warming up

If the heater is inside water then both water and calorimeter are warming up. The heat taken by water and calorimeter is:

Q_1=m_wc_w\Delta t_1+m_cc_c\Delta t_1,

where: $m_w$ denotes mass of water, $m_c$ - mass of calorimeter, $c_w$ - specific heat of water, $c_c$ - specific heat of calorimeter, $\Delta t_1$ - change of temperature of the system water + calorimeter.

On the other hand, the heat provided by the heater is equal:

Q_2=A\frac{U^2}R\tau_1,

where: $A$ – denotes the thermal equivalent of work, $U$ – voltage, $R$ – resistance of the heater, $\tau_1$ – time of work of the heater in the water.

Of course,

Q_1=Q_2.

Thus

A\frac{U^2}R\tau_1=m_wc_w\Delta t_1+m_cc_c\Delta t_1.

For petroleum in the calorimeter we get a similar formula:

A\frac{U^2}R\tau_2=m_pc_p\Delta t_2+m_cc_c\Delta t_2.

where: $m_p$ denotes mass of petroleum, $c_p$ - specific heat of petroleum, $\Delta t_2$ - change of temperature of the system water + petroleum, $\tau_2$ – time of work of the heater in the petroleum.

By dividing the last equations we get

\frac{\tau_1}{\tau_2}=\frac{m_wc_w\Delta t_1+m_cc_c\Delta t}{m_pc_p\Delta t_2+m_cc_c\Delta t_2}.

It is convenient to perform the experiment by taking masses of water and petroleum equal to the mass of the calorimeter (for that we use the balance and the sand). For

m_w=m_p=m_c

the last formula can be written in a very simple form:

\frac{\tau_1}{\tau_2}=\frac{c_w\Delta t_1+c_c\Delta t_1}{c_p\Delta t_2+c_c\Delta t_2}.

Thus

c_c=\frac{\Delta t_1}{\tau_1}\frac{\tau_2}{\Delta t_2}c_w-\left(1-\frac{\Delta t_1}{\tau_1}\frac{\tau_2}{\Delta t_2}\right)c_c

c_c=\frac{k_1}{k_2}c_w-\left(1-\frac{k_1}{k_2}\right)c_c,

where

k_1=\frac{\Delta t_1}{\tau_1}\quad\text{and}\quad k_2=\frac{\Delta t_2}{\tau_2}

denote “velocities of heating” water and petroleum, respectively. These quantities can be determined experimentally by drawing graphs representing dependence $\Delta t_1$ and $\Delta t_2$ on time ( $\tau$ ). The experiment shows that these dependences are linear. Thus, it is enough to take slopes of appropriate straight lines. The experimental setup given to the students allowed measurements of the specific heat of petroleum, equal to 0.53 cal/(g·°C), with accuracy about 1%.

Some students used certain mutations of this method by performing measurements at $\Delta t_1=\Delta t_2$ or at $\tau_1=\tau_2$ . Then, of course, the error of the final result is greater (it is additionally affected by accuracy of establishing the conditions $\Delta t_1=\Delta t_2$ or at $\tau_1=\tau_2$ ).

Source note: the source prints “water + petroleum”, an unsubscripted $\Delta t$ in the first ratio numerator, and $c_c$ on the left of both final specific-heat expressions. These printed forms are retained.

Second method: comparison of velocity of cooling down

Some students initially heated the liquids in the calorimeter and later observed their cooling down. This method is based on the Newton’s law of cooling. It says that heat $Q$ transferred during cooling in time $\tau$ is given by the formula:

Q=h(t-\vartheta)s\tau,

where: $t$ denotes the temperature of the body, $\vartheta$ - the temperature of surrounding, $s$ – area of the body, and $h$ – certain coefficient characterizing properties of the surface. This formula is correct for small differences of temperatures $t-\vartheta$ only (small compared to $t$ and $\vartheta$ in the absolute scale).

This method, like the previous one, can be applied in different versions. We will consider only one of them.

Consider the situation when cooling of water and petroleum is observed in the same calorimeter (containing initially water and later petroleum). The heat lost by the system water + calorimeter is

\Delta Q_1=(m_wc_w+m_cc_c)\Delta t,

where $\Delta t$ denotes a change of the temperature of the system during certain period $\tau_1$ . For the system petroleum + calorimeter, under assumption that the change in the temperature $\Delta t$ is the same, we have

\Delta Q_2=(m_pc_p+m_cc_c)\Delta t.

Of course, the time corresponding to $\Delta t$ in the second case will be different. Let it be $\tau_2$ .

From the Newton's law we get

\frac{\Delta Q_1}{\Delta Q_2}=\frac{\tau_1}{\tau_2}.

Thus

\frac{\tau_1}{\tau_2}=\frac{m_wc_w+m_cc_c}{m_pc_p+m_cc_c}.

If we conduct the experiment at

m_w=m_p=m_c,

then we get

c_p=\frac{T_2}{T_1}c_w-\left(1-\frac{T_2}{T_1}\right)c_c.

As cooling is rather a very slow process, this method gives the result with definitely greater error.

Source note: the final formula changes from $\tau_1,\tau_2$ to printed $T_1,T_2$ without explanation; this notation is retained.

Third method: heat balance

This method is rather typical. The students heated the water in the calorimeter to certain temperature $t_1$ and added the petroleum with the temperature $t_2$ . After reaching the thermal equilibrium the final temperature was $t$ . From the thermal balance (neglecting the heat losses) we have

(m_wc_w+m_cc_c)(t_1-t)=m_pc_p(t-t_2).

If, like previously, the experiment is conducted at

m_w=m_p=m_c,

then

c_p=(c_w+c_c)\frac{t_1-t}{t-t_2}.

In this methods the heat losses (when adding the petroleum to the water) always played a substantial role.

The accuracy of the result equal or better than 5% can be reached by using any of the methods described above. However, one should remark that in the first method it was easiest. The most common mistake was neglecting the heat capacity of the calorimeter. This mistake increased the error additionally by about 8%.

Marks and references

No marking schemes are present in my archive materials. Only the mean scores are available. They are:

Problem	Mean score
Problem # 1	7.6 points
Problem # 2	7.8 points (without the Romanian students)
Problem # 3	5.9 points
Experimental problem	7.7 points

Thanks

The author would like to express deep thanks to Prof. Jan Mostowski and Dr. Yohanes Surya for reviewing the text and for valuable comments and remarks.

Literature

[1] R. Kunfalvi, Collection of Competition Tasks from the Ist trough XVth International Physics Olympiads, 1967 – 1984, Roland Eötvös Physical Society and UNESCO, Budapest 1985

[2] Tadeusz Pniewski, Olimpiady Fizyczne: XV i XVI, PZWS, Warszawa 1969

[3] Waldemar Gorzkowski, Zadania z fizyki z całego świata (z rozwiązaniami) - 20 lat Międzynarodowych Olimpiad Fizycznych, WNT, Warszawa 1994 [ISBN 83-204-1698-1]

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