29 Pressure, Temperature relationship of a gas

Transcription

1 Chemistry Sensors: Loggers: Gas Pressure, Temperature Any EASYSENSE Logging time: EasyLog Teacher s notes 29 Pressure, Temperature relationship of a gas Read The ideal gas laws tell us that if we keep reducing the temperature of a gas then there will come point when the gas occupies no volume and has no pressure. This point is the temperature when the kinetic energy of the gas molecules will have become so insignificant that the gas molecules can exert no pressure and therefore cannot occupy any volume. This temperature is the absolute zero. Temperature is a measure of the average kinetic energy of the molecules. The zero of temperature is therefore the temperature when the molecules have zero kinetic energy. The investigation attempts to find this point by measuring the pressure of a gas at different temperatures in a fixed volume device. Plotting Pressure vs. Temperature will allow us to extrapolate the data line back to intercept the temperature axis; this intercept should be absolute zero. The investigation is a good demonstration experiment of the method, the quality of the results will vary with the experience of the investigator in selecting the data and determining a best fit line through the data. Results will vary, but values of 200 C (73K) or less should be seen as normal, higher values will indicate problems with the technique of the investigator. Apparatus 1. An EASYSENSE logger. 2. A Smart Q Gas Pressure sensor 0 to 110 kpa Absolute. 3. A Smart Q Temperature sensor. 4. Beaker, 500 cm 3 5. Constant volume device (see diagram). 6. Pressure tubing. 7. Heat source (for hot water bath). 8. Rubber stopper, two hole. 9. Small quantity of dry silica gel (optional). Notes The Gas Pressure sensor has temperature compensation built in (0-50ºC), this increases accuracy of the pressure readings as the ambient temperature changes. For this experiment the compensation can prove to be problematic, when the ambient temperature falls below (10ºC). For this reason it is best to organise the sensor to be external to the heat source used. You will notice when the compensation is failing as a curve starts to appear in the data when a pressure vs. temperature plot is made. For analysis use the straight line section. T29-1(V2)

2 We found that better curves were obtained for falling temperatures. Using a temperature range between about 60ºC and 10ºC will give good data for analysis. To use the maximum range it will be necessary to heat up the Constant Volume device with the pressure lead open so that the pressure inside the apparatus is at atmospheric pressure at the maximum temperature used. The Pressure sensor is connected once the maximum temperature is reached, and the temperature is steady. If the Pressure sensor is attached before the Constant Volume device is heated to its maximum temperature, the pressure will be above atmospheric pressure (about 100 kpa at sea level). The sensor cannot work above 110 kpa. This will limit the maximum temperature that can be used. In this case, the kpa sensor should be adequate up to temperatures of 20 to 30 degrees Celsius above the ambient temperature, at sea level. If working above sea level then the upper temperature that can be used is higher. For example at a height of 500 m an upper temperature of about 40ºC above ambient temperature should be alright. In the sample data we used a temperature range of 6ºC to 24ºC. We found that starting at 24ºC, and then cooling the air in cold water, worked well. The theory assumes the gas is acting as an ideal gas. The sample of air being used for the investigation will contain water vapour; this does not act as an ideal gas. When the water vapour reaches its condensation point it will move rapidly from the gas to liquid phase. This transition will create a disjunction in the data seen as a curve in the data as it approaches lower temperatures. Ideally the air sample should be dry; adding some silica gel to the air reservoir some time before readings take place will help to remove any water vapour and will give a reduction in errors. Alternatively a dry air source, such as bottled air could be used to fill the apparatus. How much attention is paid to this will depend on how the investigation is being used. Constant volume device Alternative 1 A constant volume device can be made from a 22 mm copper (or iron) T piece with two of the ends blanked off using soldered end caps. The shape of the device means that the temperature sensor can be placed in a more central region of the device. Soldered end caps Iron pipe T Rubber bung Rubber bungs Drinking straw Iron pipe T The bung that goes into the remaining opening on the device has two holes. One of the holes allows the Temperature sensor to reach the inside of the device. The second hole has a glass delivery tube or rigid plastic tubing fitted; this allows a piece of 3 mm plastic tubing to connect to the Pressure sensor. A rubber bung and slightly undersized holes for the sensors ensure a good airtight fit. When fitting the Temperature sensor and the delivery tubing a small quantity of silicone grease, liquid soap or glycerine helps lubricate the holes and make insertion easier. It is best to have the glass / plastic tubing pre-fitted. An alternative is to use pneumatics tubing 3 mm in size. This tubing is made from rigid polyurethane and can be inserted into the bung directly. A small piece of plastic aquarium tubing is needed to connect the rigid tubing to the Pressure sensor. If a quick fit T connector is used, an unhoused T29-2(V2)

3 Temperature sensor can be modified to fit the connectors and passed through into the constant volume device. Refer to figure below for details. Heat shrink Silicon sealant 3mm stiff plastic or glass sleeve Adding a small quantity of a water absorbing material (e.g. silica gel) can alter the quality of the results. The presence of water vapour can give results that undervalue the absolute zero by quite a large margin. Leave the apparatus sealed with the silica gel inside for 10 minutes or longer if possible before starting the experiment. Experience has shown that a slow gentle cooling gives better results than a rapid cooling. Alternative 2 You can make a constant volume device using a spherical ball valve float approximately 12 cm diameter (as used to control water levels in a water tank). Threaded pneumatics t Pneumatics Tee connector The ball valve float has had a threaded pneumatics control quick fit connector fitted to the point where the ball valve would connect to its control arm. This allows a piece of pneumatics tubing to be connected to the ball valve, a t piece is used to then connect a Pressure sensor. An unhoused Temperature sensor (modified as in the instructions above) is fed into the ball valve float to a position of equal distance from all the sides. Using this method the float could be placed into a fridge with the Pressure sensor outside the fridge (this prevents the temperature compensation of the sensor from working). The change in temperature and pressure can be recorded. Set up of the software and logger Use EasyLog, the length of the experiment is variable; you should aim for a long heating time. Analysing the data The data analysis has three stages; 1. Adjusting the plot 2. Adjusting the axis scales. 3. Calculating Absolute zero. T29-3(V2)

4 Sample results A typical set of results obtained using a 22mm copper T piece apparatus Time (ss) Graph 1 - showing data as collected, apparatus cooling from hot Stage 1: Plot the data as a x, y plot 1. Click on Options and select the X Axis tab. Select Channel as the X-axis. 2. Click outside the graph area to select the horizontal axis (x) as Temperature and the vertical axis (y) as Pressure Temperature ( C) Graph 2 - showing data as a Y vs. X plot T29-4(V2)

5 Stage 2: Adjusting the axis scales 1. Click on Options and select the Sensor settings tab. 2. Adjust the temperature range to have a minimum value of Adjust the pressure range to have a minimum of Graph 3 Temperature axis limits set to 300ºC Temperature ( C) Stage 3: Finding Absolute Zero. The data may be analysed by graphical methods, or by calculation. Absolute zero by Graphical methods Drawing the line of best fit manually Use File, Print Graph to print a hard copy of the data. Use a ruler / straight edge to line draw a best fit line through the graph line and extend this back to intercept the temperature intercept. The intercept with the x axis is your experimental value for Absolute Zero and represents the point of zero pressure for the gas. Graph 4 Using a manually drawn best fit line to extrapolate data back to pressure = 0. Gives a result of about 280ºC. T29-5(V2)

6 Drawing the line of best fit in the EasySense software Right click on the graph area, and select Zoom In. Select the area where the curve is. From the Tools menu select Best Fit, Select Manual and draw the line of best fit on the straight line section of the graph Graph 5 Best Fit line fit (Manual) applied to the straight line section of the curve y = 0.327x Temperature ( C) Using the values of the curve as shown: y = 0.327x When Pressure = 0, then y = 0 0 = 0.327x x = x = -276ºC Absolute zero by calculation 1. Find the highest temperature (maximum for x ) and the highest pressure (maximum for y ). Enter these values into the results table. 2. Find the lowest temperature (minimum x ) and the lowest pressure (minimum y ). Enter these values into the results table. Results table T1 Measurement Highest temperature Value 0 C P1 Highest pressure kpa T2 Lowest temperature 0 C P2 Lowest pressure kpa C Y-coordinate of intercept kpa T29-6(V2)

7 Calculations 1. Use the formula below to find the slope of the data: = Δy = P 1 Slope ( m ) P 2 Δ x T 1 T 2 (Calculation 1) 2. Use the general formula of a straight line to find the value for Absolute Zero ( x in the formula below): Y = mx + c Y = (calculation 1)x + c Since Y = 0 at the Y intercept, x c = Calculation 1 (Calculation 2) T29-7(V2)