Overview
The primary purpose of the Gases simulation is to teach the concepts and fundamental principles that led to an understanding of the properties of gases. As is usually the case, these concepts and principles were discovered or elucidated by a series of experiments that were developed and carried out over a period of many years by some of the great minds of the 18th and 19th centuries. Modern experiments involving gases most often require equipment that is not readily available in typical instructional laboratories.
At the Gases lab bench, experiments are performed in a framework where students are put into a virtual environment where they are free to choose their equipment and build a conceptual experiment of their own design and then experience the resulting consequences. The focus in the Gases simulation is how the four variables that are used to describe gases, namely pressure, volume, temperature, and the number of moles, are related to and affect each other. An additional focus of the simulations is to investigate the differences between ideal, van der Waals, and real gases. The observation and manipulation of data to make conclusions about the behavior of gases is the ultimate goal of these simulations.
In general, the simulated in Gases are based on the interdependence of the four variables used to describe and represent the properties of gases (P, V, T, and n). The simulation contains four experiments, each of which focuses on a different variable as the dependent variable (except for n which is always an independent variable). The individual experiments are identified in the stockroom using signs placed underneath four separate hoist controllers. The hoist controllers are used to select and bring out to the laboratory an experimental apparatus corresponding to one of the four experiments. The labels on the signs have the form "V = f (P,T)," which, for example, indicates that the volume is the dependent variable and pressure, temperature, and the number of moles are the independent variables. The four experiments in the simulations are (1) V = f (P, T) (balloon), (2) P = f (V, T), (3) T = f (P, V), and (4) V = f (P, T) (cylinder). Both the first and last experiments have volume as the dependent variable, but the first experiment uses a balloon to reflect the changes in volume and the last experiment uses a frictionless, massless piston. Details on these experiments and the assumptions used in the simulation are given below. A description of the gases and the equations of state used in the simulations are also given.
Experiments
V = f (P, T); The Balloon Experiment. In this experiment, a balloon is used to reflect the changes in volume as the pressure, temperature, or number of moles are adjusted. The balloon is considered to be a perfect balloon in that it exerts no pressure on the gas inside. In other words, the balloon is a perfect transfer medium for the external pressure in the experimental chamber. Adjusting the pressure and temperature changes the pressure and temperature of the inert, ideal gas inside the chamber. Changing the number of moles changes the number of moles of the select gas inside the balloon.
P = f (V, T); The Pressure Experiment. In this experiment, a motor driven piston is used to change the volume and a pressure transducer is used to measure the resulting effects on the pressure. The temperature of the cylinder can also be adjusted. Changing the number of moles changes the number of moles of gas inside the cylinder. The volume of the cylinder can be adjusted between 0 and 4 L. There are no significant assumptions made in this experiment.
T = f (P, V); The Temperature Experiment. A motor driven piston is used again to change the volume, but in this experiment the resulting temperature change is measured as a consequence of the volume and pressure changes. This is actually a somewhat virtual experiment since there is no practical method available to change the pressure in a constant volume, constant mole experiment or to change the volume keeping the pressure and number of moles constant. The purpose of this experiment, however, is to show the effects on temperature as the pressure, volume, and number of moles are changed.
V = f (P, T); The Cylinder Experiment. This experiment is similar to the balloon experiment in that the volume is dependent on changes in pressure, temperature, and the number of moles of gas. However, in this experiment, the selected gas (ideal, real, or van der Waals) is added to the experimental chamber and then a sample of gas is trapped in the cylinder when a frictionless, massless piston is placed on top of the cylinder. The number of moles of gas trapped in the cylinder is determined by the temperature and pressure of the gas in the chamber at the time the piston is placed on the cylinder. The walls of the cylinder are rigid, consequently, pressure can only be exerted on the gas in the cylinder through the piston. This is accomplished by either adjusting the external pressure of the gas in the chamber or by placing weights on the piston. The piston can only be removed when there are no weights on the piston and when the piston is at the top of the cylinder. The only assumption in this experiment is that the piston is both frictionless and massless. For some calculations it will be necessary to know that the cylinder diameter is 15 cm and the cylinder height is 40 cm.
Gas Equations
The gases that can be used in the four experiments include an ideal gas; a van der Waals gas whose a and b parameters can be adjusted to model any real gas; and the real gases N2, CO2, CH4, H2O, NH3, and He. In addition, mixtures of ideal gases of varying molecular weights can also be added to the balloon experiment, the pressure experiment, and the temperature experiment.
When an ideal gas is used in any of the experiments, the ideal gas equation, PV = nRT, is used to perform the necessary calculations for the pressure, volume, and temperature. Similarly, when a van der Waals gas is used in the experiments, the van der Waals equation of state, [P+a·(n2/V2)](V-nb)=nRT,is used to perform the calculations where the a and b parameters must be in units of L·atm. For ideal gas mixtures, Dalton's Law of Partial Pressure is used to calculate the partial pressure of each gas in the mixture. For the real gases, the most accurate and sophisticated equations of state available were used in the calculations. The equation of state specified in The NBS/NRC Steam Tables (L. Haar et. al, Hemisphere Publishing, Washington, 1984) was used for H2O, and the equations of state found in Thermodynamic Properties in SI (W.C. Reynolds, Stanford University, Stanford, 1979) were used for the remaining real gases.
The actual limits of validity of the real equations of state, as implemented in the simulation, are quite complicated; but, in general terms, the equations are generally valid from the triple point, following the liquid-vapor line to the critical point, and then into the supercritical region to a relatively high temperature and pressure. For the real gases, these maximum pressure and temperature limits are as follows: N2, 200 MPa and 1200 K; CO2, 20 MPa and 1000 K; CH4, 4.5 MPa and 400 K; H2O, 1500 MPa and 1273 K; NH3, 20 MPa and 660 K; and He, 100 MPa and 1500 K. Both the ideal gas and van der Waals gas are valid up to 1000 MPa and 3000 K in the simulation.