The vertical-syringe problem. A syringe that contains an ideal gas and has a frictionless piston of mass is moved from an ice-water bath to a beaker of boiling water, where it comes to thermal equilibrium. Students are asked if the final pressure and volume of the gas are greater than, less than, or equal to the initial pressure and volume, respectively. They are asked to explain their reasoning.
The three-cylinders problem. Three identical cylinders are filled with unknown quantities of ideal gases. The cylinders are closed with identical frictionless pistons of mass . Cylinders A and B are in thermal equilibrium with the room at , and cylinder C is kept at a temperature of . The students are asked whether the pressure of the nitrogen gas in cylinder A is greater than, less than, or equal to the pressure of the hydrogen gas in cylinder B, and whether the pressure of the hydrogen gas in cylinder B is greater than, less than, or equal to the pressure of the hydrogen gas in cylinder C. They are asked to explain their reasoning.
The insulated-cylinder problem. A cylinder with a frictionless piston contains an ideal gas. The cylinder is placed in an insulating jacket and small masses are added. The students are asked whether the pressure, temperature, and volume of the gas will increase, decrease, or remain the same. They are asked to explain their reasoning.
Schematic diagram of laboratory apparatus.
The double-chamber problem. A cylinder is divided into two chambers by a freely sliding piston of mass . In each of the situations, both chambers contain unknown amounts of ideal gases and the piston is at rest. Both gases are at the same temperature. The students are asked to compare the pressures of the gases in the two chambers and to explain their reasoning.
The two-cylinders problem. Two identical cylinders with frictionless pistons contain an equal number of moles of the same ideal gas at the same pressure. Cylinder 1, which has a piston of mass , is at room temperature. Cylinder 2 is at a temperature of . The piston that closes cylinder 2 is not shown. In the bottom diagram are three movable pistons of different masses that fit cylinder 2. Students are asked to choose the correct piston (A, B, or C) for cylinder 2 and to explain their reasoning.
Results from the vertical-syringe problem (Fig. 1).
Results from the three-cylinders problem (Fig. 2).
Results from the double-chamber problem (Fig. 5) after different types of instruction at UW. The percentage gives the fraction of students who correctly compared pressures with correct reasoning for each situation.
Results from the two-cylinders problem (Fig. 6) after different types of instruction at UW.
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