Teacher s notes 15 Temperature volume relationship in a gas (Charles law, Gay-Lussac s law)

Size: px

Start display at page:

Download "Teacher s notes 15 Temperature volume relationship in a gas (Charles law, Gay-Lussac s law)"

Ginger Wilcox
5 years ago
Views:

Sensors: Loggers: Temperature, Rotary Motion Any EASYSENSE Physics Logging time: EasyLog Teacher s notes 15 Temperature volume relationship in a gas (Charles law, Gay-Lussac s law) Read The

1 Sensors: Loggers: Temperature, Rotary Motion Any EASYSENSE Physics Logging time: EasyLog Teacher s notes 15 Temperature volume relationship in a gas (Charles law, Gay-Lussac s law) Read The relationship between gas volume and temperature is studied in this investigation. The plot of the data as an x y plot shows the linear nature of the relationship. Historically, in 1802 Gay-Lussac was the first to show that the law applied to all gases, although he credits the discovery to unpublished work in the 1780s by Jacques Charles. The law was also discovered, independently, by John Dalton in Gay-Lussac s statement of the law is:- V 100 V 0 = kv 0 The value of k is the same for all gases The plot of volume vs. temperature should have an intercept of zero volume = absolute zero. In the analyses described in the student s sheet the value of absolute zero is revealed in the answer to calculations, or by graphical methods. The investigation should allow the students to, 1. Model the determination of absolute zero. 2. Showing the linear relationship between volume and temperature for a gas. Understand the modern statement of Charles law given below: Charles' law states that the volume of a given amount of dry ideal gas is directly proportional to the Kelvin Temperature provided the amount of gas and the pressure remain fixed. When we plot the Volume of a gas against the Kelvin temperature it forms a straight line. The mathematical statement is that V / T = a constant. V 1 / T 1 = V 2 / T 2 The graph data should provide evidence of this relationship. Apparatus 1. An EASYSENSE logger 2. A Smart Q Temperature sensor (unhoused if possible). 3. A Smart Q Rotary Motion sensor set to the linear distance range. 4. A RMS linear rack attachment. 5. Large flask (250 cm 3 minimum). 6. Bung with two holes, one hole fitted with glass or plastic delivery tube. 7. Gas syringe 100 cm 3 capacity. 8. Water bath. 9. Bunsen or other heater for water bath. T15-1 (V2)

2 Set up of the software There is no need for a software setup with this experiment. As the duration of the experiment is unknown it is best to use EasyLog. Notes The investigation produces the best results if the heating of the apparatus is not too rapid. If the apparatus is left in the water bath and allowed to cool the cooling curve will often give better results, but it can take a long time to cool. The gas syringe should be cleaned before use and checked to see the plunger moves easily along the barrel of the syringe. Wiping with a clean cloth dampened with acetone removes most oily materials from the plunger, but make sure the acetone has completely evaporated before refitting the plunger to the barrel. A temperature of 100 C is not needed in the apparatus as the results can be extrapolated to find the 100 C value and the 0 oc value, however taking the temperature to 100 C makes analysis easier. Errors The gas used may contain water vapour, as this is not an ideal gas, the results will be strongly affected by its presence. To remove the water vapour Silica Gel can be placed into the apparatus and left for about an hour before use. The gas cools as it enters the syringe and the volume decreases, careful observation in the course of the investigation will show the plunger advancing and then retreating slightly. The cooling curve is not affected by this as much as the gas is moving back into the flask. There is no easy method to eliminate this, you could try wrapping the barrel of the gas syringe with insulating material e.g. bubble wrap. At this level of work it may be better to use the experiment as a model and leave the errors present, discussion of the potential sources of error can be more valuable than the collection of a an accurate result at this stage of learning. Sample data and analysis Data collected will be Linear distance and Temperature vs. Time 1. Convert linear distance to volume. a. The Linear rack measurements need to be only positive. If necessary use the Post-log Function, General, Tare to achieve this. It is impossible to have negative values of Volume. b. Use Test Mode, Meters (in software) or Meters on the logger. Find the linear rack measurement when the syringe plunger is fully in (this represents 0 volume + Volume of apparatus) and when the plunger has moved out to the end of the gas syringe scale. Use this to calculate the correction (in cm 3 /mm) for linear rack to volume in syringe. You may be lucky and find they are both the same c. Apply the correction to the linear rack data by using Post-log Function, General, Multiply by a constant. Give the new data the name Volume and units cm3. T15-2 (V2)

3 2. Add the volume of the apparatus to the change in Volume data. a. Find the volume of the apparatus, by filling with water and either using increase in mass or recording volume. Use 1 g =1 cm 3. (for more precision check data tables for water density at the experimental temperature) b. Add this volume to the Volume data created by using Post-log Function, General, Add a constant. Give the new data the name Total volume. The graph below shows the Total Volume and Temperature plotted against Time. Plotting the data 1. Select Options and click on the X-Axis tab. Select Channel as the x axis. 2. Click on OK 3. Click in the space to the side / below the axis scale to change the axis to be Volume on the y axis and Temperature on the x axis. Use Zoom to enlarge the graph. The sample graph is shown below: T15-3 (V2)

4 Historical approach to calculating Absolute Zero Historically the graph of the data was used to estimate the values of the Volume at 0 C, and 100 C. These values were then used to calculate the value of T the Absolute Zero. The diagram below shows the data graph extrapolated to obtain an intercept on the Temp axis for when Volume = 0 Volume V 100 V 100 V 0 V V 0 Temperature ºC T 0,0 100 C The gradient of the graph T 100 V0 = ( V 0 ) V 100 Absolute Zero T = (Volume at 0 C x 100) (Volume change 0 C to 100 C) NOTE: From Gay-Lussac s equation on page 15T-1 we get: k = (V 100 V 0 ) V 0 T = 100 k If the temperature data has not reached 100 C or 0 C there are two ways to obtain these values. 1. Manually: You will have to print out the graph and use a pencil and ruler to draw a best fit line extrapolated back to 0 C and to 100 C. You will need to find the temperature and volume at the two temperatures. 2. Use the equation of the graph Draw a Best Fit line (Tools menu). T15-4 (V2)

5 Use the Best fit line. The equation of the Best Fit line will be displayed. It will look like this y = 0.???x +???? (e.g. y = x ) equivalent to y =mx + c. NOTE: y is the Volume, and x is the temperature in C The last number (the c value) is intercept of the y axis when x = 0, and gives us the volume of the apparatus when the temperature is zero. Calculate the value of y when x = 100. This will give the value of the volume at 100 C. Calculate absolute Zero by, Absolute Zero T = (Volume at 0 C x 100) (Volume change 0 C to 100 C) In the sample data experiment the Temperature of an apparatus containing 250cm 3 of air was raised to 103 C. The data was recorded as above, and treated in the same way as described. The best fit line gave a line whose equation was y = 0.812x The volume at 0 C was therefore 228.0cm 3 The volume at 100 C was cm 3 Volume change was = 82.3 Solving, Absolute Zero T = (Volume at 0 ºC x 100) (Volume change 0 C to 100 C) = (228.0x 100) 81.2 = -281 C Alternative approach using modern graphing Using the equation of the Best Fit Line: y = 0.812x Putting in the symbols for Volume (V) and temperature (t): V = 0.812t T15-5 (V2)

6 If V = 0 then: 0.812t = Rearranging: t = t = ºC Extrapolating manually From the Display menu select Sensor settings. Change Total Volume to 0 to just above the maximum value of the Total Volume. Change the temperature to -350 C to 100 C. You will get a graph like the one below. Temperature is the x axis. T15-6 (V2)

15 Temperature volume relationship in a gas (Charles law, Gay-Lussac s law)

15 Temperature volume relationship in a gas (Charles law, Gay-Lussac s law) Sensors: Loggers: emperature, Rotary Motion Any EASYSENSE Physics Logging time: EasyLog 15 emperature volume relationship in a gas (Charles law, Gay-Lussac s law) Read he French scientist Jacques Charles