AE 3051, Lab #16 Investigation of the Ideal Gas State Equation By: George P. Burdell Group E3 Summer Semester 20001 Abstract The validity of the ideal gas equation of state was experimentally tested for three gases: helium (He), argon (Ar) and nitrogen (N2). The experiments were conducted in a fixed volume container over a range of pressures (~30-60 kPa) and temperatures (~295-360 K). Gas temperatures were determined with a type-K thermocouple, and the pressures were measured with a mercury manometer. The measurements for each gas were obtained with a single, fixed gas sample; thus each sample had a constant mass. In agreement with the ideal gas law for these conditions, the density ratio, p/RT, was found to be constant, at least within the ~6% uncertainty of the measurements. The uncertainty in p/RT was primarily a result of the repeatability of the pressure and temperature conditions, which could be improved by more carefully ensuring that steady-state is achieved.2 Introduction An important relationship often used to relate specific gas properties is the ideal gas equation of state. This report describes experiments intended to investigate the validity of this state equation, which can be written as RTp , where p is the absolute pressure, T is the absolute temperature and R is the specific gas constant. In order to verify the ideal gas state equation, the pressure of a fixed gas sample was measured as it was heated in fixed volume container. Three individual gases: helium (He), nitrogen (N2) and argon (Ar), were tested. The temperature and pressure inside the container were measured with a thermocouple and a mercury manometer. In addition, the volume of the container was determined by measuring an equivalent volume of water. Experimental Setup Figure 1 illustrates the experimental apparatus employed in this investigation. The fixed- volume, aluminum test cell is composed of a cylindrical body and two end flanges. There are three connections to the cell: the first connects the cell to a control valve and to the high pressure cylinder containing the test gas; the second connects to another control valve and a vacuum pump; and the third connects the cell to a vertical-type mercury manometer. The test cell tubing attaches to the top of the vertical arm of the manometer, while the mercury bath is open to the atmosphere. Mounted vertically, alongside the manometer, is a ruler, which has a fine scale marked in 1/32 units. The apparatus also includes a digital barometer for measuring the local atmospheric pressure in the room. Electrical-resistance heating tape wrapped around the cell controls the cell’s temperature, as well as the temperature of the gas inside. The voltage across the heating tape, and therefore the3 current through it, is regulated by a variable transformer. A type-K thermocouple passes through the side of the cell and monitors the temperature of the gas inside. The thermocouple leads connect to a calibrated electronic readout unit that includes an electronic reference junction. In order to ensure that the gas temperature is nearly uniform inside the test cell, the cell is covered with insulation. In addition, there is a stirring mechanism at the bottom of the cell that is magnetically-coupled to a motor outside the cell. High Pressure Gas Cylinders Vacuum Pump patm p Valve Mercury Manometer Test Cell Type-K Thermocouple Thermocouple Readout Magnetic Stirrer Heating Tape Figure 1. Schematic of the experimental apparatus. In order to measure the volume of the cell, the top flange was removed and the cell was filled with water. The water was then emptied into a 100 ml graduated cylinder. After drying the cell carefully, the flange was replaced and tightened. Then the vacuum pump was turned on for a period of 20 minutes so as to empty the cell of air. For each test gas, the following measurement procedure was employed. First, the cell was evacuated with the vacuum pump to a gauge pressure below 29.7 in. Hg. Then, the cell was pressured to ~1 atm with the test gas (at approximately room temperature). This cycle of filling and evacuating was repeated three more times to ensure the cell’s contents were limited to the test gas of interest. Then, the test cell was4 filled to a pressure below 1 atm, the magnetic stirrer was activated, and the thermocouple readout was monitored until it did not change by more than 0.1C in 10 seconds. With the container at steady-state, the pressure and temperature readings were acquired. Next, the voltage on the heating tape was then increased a small amount, and the pressure and temperature measurements were taken again after the thermocouple readout stabilized. Results and Discussion As noted above, the test cell’s volume was ascertained by filling the test cell with water and measuring the water volume with the graduated cylinder. This process was repeated a total of 10 times and the results are shown in Table I. The average of the ten measurements is 83 ml, or equivalently, 83 cm3. Next, the lab group measured the atmospheric pressure using the digital barometer. The measured pressure was 29.66 in. Hg. Table I. Test cell volume results determined from equivalent volume of water. Sample # Volume (ml) 1 83.0 2 83.0 3 82.5 4 83.0 5 83.0 6 83.5 7 83.0 8 82.5 9 83.0 10 83.0 Initially, six measurements of cell gauge pressures as a function of temperature were taken for each gas. The results are listed in Table II for all three gases (He, N2 and Ar). The measured temperatures and pressures can be converted to absolute values using the following conversions:5   273 CTKT (1)       Hg.inmmHg.mmHgPaHg.inpHg.inpPapatmgage1425760101325 . (2) With the measured atmospheric pressure in the test room, Equation (2) reduces to:     66293386 .Hg.inpPapgage (3) The raw data listed in Table II were converted to absolute values using Equations (1) and (3). They are shown plotted in Figure 2. For all three gases, the data shown in Figure 2 appear to fall along a single line in p,T space. This agrees with the ideal gas state equation, i.e., p=constantT, which is the equation for a line going through the origin. Table II. Pressures and temperatures for 3 gases in a heated, fixed volume