Research on student understanding of the ideal gas law

Research on student understanding of the ideal gas law
Christian H. Kautz, Michael E. Loverude, Paula R. L. Heron, Lillian C. McDermott
Department of Physics, University of Washington


Abstract. The Physics Education Group at the University of Washington has been
investigating student understanding of thermal physics. In this paper, our focus is on
the ideal gas law. Analysis of student responses in interviews and on written tests
administered in first-year and second-year undergraduate courses indicates that
after instruction many students are not able to interpret and apply the ideal gas law.
In particular, difficulties with pressure, volume, and Avogadro’s law are prevalent.
Results of this study also suggest that difficulties with mechanics and incorrect ideas
about the particles and processes at the microscopic level often interfere with the
development of a coherent understanding of this topic. Information obtained in this
study is being used to guide the design of instructional materials for the introductory
university level.
Introduction. The ideal gas is a standard topic in courses in physics and chemistry
at the introductory university level. First, it is important as an approximation to the
behavior of real gases. Furthermore, it serves as a context for introducing the
concepts and laws of classical thermodynamics. Instruction on the ideal gas usually
includes both microscopic and macroscopic aspects of this topic.
Previous research. Many studies of student understanding of gases have focussed
on children’s difficulties with the particle model [1,2,3]. A study carried out with
introductory university students and in-service teachers in France suggests that even
adults have difficulty reasoning about thermal properties of gases, both at the
microscopic and macroscopic levels [1].
Context. This ongoing study has involved more than 1500 students at the University
of Washington (a major public research university with a competitive admission
policy) and at comparable institutions. The students were enrolled in three types of
courses: algebra-based introductory physics courses for students majoring in the life
sciences (including pre-medical studies), calculus-based introductory physics
courses for students majoring in the physical sciences and engineering, and a
second-year thermal physics course in which students majoring in physics account
for about a third of the enrolment.
Goals. Our aim was to investigate the extent to which students receiving traditional
lecture instruction develop a functional understanding of the ideal gas law (IGL). We
define a functional understanding as the ability to interpret and apply the IGL. This
requires the student (1) to identify the quantities in the IGL and relate them to a
physical situation, and (2) to use the IGL to make predictions or comparisons about
these quantities in one or more samples of gas. In particular, we sought to identify
specific difficulties that students have with the material.
Methods. The methods used in this study have included exploratory student
interviews and written questions. Interviews with individual students allowed us to
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probe their understanding in detail. Results from the interviews then guided the
design of open-ended written questions that have been administered to a large
number of students.
Interviews. Two sets of student interviews were carried out over a period of 15
months, with a total of 50 students. Each set centered on a protocol involving a
different physical situation. One required the student to make predictions about
isobaric and adiabatic changes of a given gas sample; the other, to make
comparisons between samples of different types of gas.
Written questions. We posed a number of written questions in order to estimate
the prevalence of the student difficulties our interviews had revealed. Some of the
written questions were part of scheduled course examinations. Others were given as
ungraded quizzes after the relevant material had been covered in lecture.
Results. Analysis of student answers in interviews and on written questions showed
that many students had difficulty interpreting some of the variables in the IGL. In
addition, students often failed to apply correctly the relationship between the
variables that is expressed by the IGL. Some of our observations confirm results
that have previously been reported in the literature [4].
Interviews. The interviews led us to the following preliminary conclusions: Many
students are unable to apply the definitions of pressure or volume to a physical
situation. Some students also seemed to believe that the molar mass of the gas
affects the number of molecules in a given volume (in contradiction to Avogadro’s
law). In many cases, students based their predictions on incorrect microscopic
models of the ideal gas. In particular, we found the belief that collisions between
particles bring about changes in temperature to be widely held. The interviews also
confirmed that many students had difficulty reasoning with more than two variables.
Finally, the students’ arguments, both at the microscopic and the macroscopic levels,
often revealed deficiencies in their understanding of mechanics.
Written questions. Results obtained from written questions substantiated the
conclusions from the interviews. Below we briefly describe some of the specific
student difficulties that we observed.
Difficulties with pressure: Many students at all three levels failed to apply the
definition of pressure (P=F/A) in situations in which the external conditions of
different gas samples were equivalent. Instead, students incorrectly attributed
different pressures to the samples because of their different temperatures, volumes,
or types of gas. Other students attempted to relate the pressures to the external
conditions but failed to do so correctly. In many cases, difficulties with Newtonian
mechanics prevented students from arriving at a correct answer.
Difficulties with volume: Some students in the algebra-based introductory course
had incorrect ideas about volume. In particular, even some of the stronger students
in the class seemed to fail to distinguish between volume and the amount of gas.
Difficulties with Avogadro’s law: When asked to compare the number of molecules
of different (ideal) gas samples at equal pressures, volumes, and temperatures,
more than a quarter of the students in the thermal physics course failed to recognize
that the number of molecules must be equal by Avogadro’s law (or by the ideal gas
law).
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Difficulties with pressure and temperature in the microscopic model of ideal gases:
Answers to written questions confirmed the result from interviews that many students
believe that collisions between molecules account for increases in temperature.
Many students also tend to associate a greater density of particles with higher
temperature. Incorrect ideas that students have about particles and processes at the
microscopic level account for some of the difficulties with Avogadro’s law.
Conclusions. We have found that many students receiving traditional lecture
instruction fail to develop a functional understanding of the ideal gas law in several
respects. Students have difficulty (1) relating the quantities in the ideal gas law to a
given physical situation and (2) making predictions and comparisons about one or
more gas samples on the basis of the ideal gas law. The data suggest that incorrect
ideas that students have about the particles and processes at the microscopic level
often contribute to their difficulties with this material. Furthermore, difficulties with
mechanics may impede the development of an understanding of thermal physics.
We have begun to use the research results described in this paper to guide the
development of curriculum to address the specific difficulties that we have found.
Preliminary results indicate that such special instruction can help address student
difficulties.
References.
[1] Driver, R. (1983). An Approach to Documenting the Understanding of 15 years
old British Children about the Particulate Theory of Matter. In: Proceedings of the
International Workshop on Research in Physics Education, La Londe les Maures,
France.
[2] Nussbaum, Joseph (1985). The Particulate Nature of Matter in the Gaseous
Phase. In: R. Driver, E. Guesne & A. Tiberghien (Eds.). Children’s ideas in science.
Milton Keynes: Open University Press.
[3] Séré, M. G. (1985). The gaseous state. In: R. Driver, E. Guesne & A.
Tiberghien (Eds.). Children’s ideas in science. Milton Keynes: Open University
Press.
[4] Rozier, S. and L. Viennot (1991). Students' reasonings in thermodynamics, Int. J