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

Transcription

1 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 was an early balloonist, he wanted to understand why the gas in the balloon enabled him to fly. He studied the relationship between the volume of a gas and its temperature, as the balloons he had flown used hot air to fly. In this investigation you will study the relationship between the temperature of air and its volume. he work of Charles was later refined and published by Gay-Lussac. You will also work out a value for the Absolute Zero of temperature. It is the lowest possible temperature. If a gas could exist at this temperature its volume would be zero. In practice all gases liquefy above this temperature. o datalogger emperature sensor Delivery tube Syringe 100cm 3 Rack attachment Bung Retort stands Rotary Motion sensor Note: For best results there should be a water bath surrounding the flask, this keeps the temperature increase in the flask more constant. Input 1 Input 2 emperature Rotary Motion What you need 1. An EASYSENSE logger. 2. A Smart Q emperature sensor. 3. A Smart Q Rotary Motion sensor set to the linear distance range 4. 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 (2)

2 What you need to do 1. Assemble the apparatus as shown in the diagram. Make sure the track attachment touching the syringe is correctly aligned to give a free movement of the plunger and rod. he bung will need to be out of the apparatus to test this. Use a piece of Blu ack or something sticky to fix the rack attachment to the syringe plunger. 2. Set the plunger to the zero point on the syringe scale. 3. From the EasySense software s Home screen select EasyLog. 4. Click on ools and select est Mode, Press the Zero button on the Rotary Motion sensor and make a note of the distance, you will need this to make a correction later. 5. Move the plunger out to the 100 cm 3 mark. Make a note of this distance, push the plunger back to zero. 6. Place the bung into the flask and note the temperature in the flask. Stop est Mode. 7. Light the Bunsen and place under the apparatus, have the flame small. You want to heat the apparatus slowly to allow the heat to transfer from the flame to water in the bath to air in the flask. 8. Click on the Start to start the logging. 9. Keep a watch on the apparatus to make sure the plunger does not come out of the syringe. If the plunger reaches the maximum of the syringe scale stop the logging. 10. Remove the heat from the apparatus, and leave the apparatus alone 11. When the logging has stopped click on Options, click on X-Axis and select Channel as the X axis. his will allow you to produce a graph of emperature vs. Distance. he graph should be approximately a straight line. If it isn t you will need to repeat the experiment. he most likely reason for a curved line is heating the apparatus too quickly. 12. Save the data and click on Start to collect the data when the temperature is falling in the apparatus. Stop the recording when the syringe volume is back to zero. 13. When you have collected all the temperature pressure data. Fill the flask with water and use a measuring cylinder to find the volume of the flask. Results and analysis You will need to:- 1. Calibrate the linear distance to read volume. 2. Calculate the otal olume of gas 3. Plot the data as an x y plot. hen find the Absolute Zero by one of two methods:- Using an historical approach Using modern graphical analysis. 1. Calibrating the linear distance to read volume he Linear rack measurements need to be only positive. If necessary use the Post-log Function, General, are to achieve this. It is impossible to have negative values of olume. Using your results, from steps 2 to 4 above, to find out how much distance is recorded when the syringe goes from 0 cm 3 to 100 cm 3. his will give the mm of linear distance for 100 cm 3. Calibration factor n = 100 Linear distance (from 0 cm 3 to 100 cm 3 graduations) n is in cm 3 / mm 1. In ools select Post-log Functions. 2. Select function General, Multiply by a constant. 3. Select data channel Linear Rack 4. Name - olume. 5. Unit cm3 (note you cannot enter superscripts) 15-2 (2)

3 6. Dec Places Number to multiply by = n from above calculation. 8. Click on OK to produce the new data channel. 2. Calculate the otal olume of the Gas You need to add the volume of the flask to the olume data created above, to obtain the otal olume of the gas in the apparatus. 1. Select Post-log Functions, General, Add a constant 2. Select data channel olume 3. Name otal volume 4. Unit cm3 5. Number to add the measured volume of the flask 6. Decimal places 1 7. Click on OKk to produce the new data channel. 8. Click on Display, Sensor Settings. Change otal olume Min to 0, click on OK. 3. Plot the data as an x y plot 1. Click on Options and select the X-Axis tab. 2. Select Channel as the X-Axis. 3. Click on the axis labels to select the horizontal axis as emperature and the vertical axis as otal volume. he historical calculation hese calculations require us to have the volume at 100 C and 0 C. o find this information the graph line needs to be extrapolated. 1. Click on the Display menu. 2. Select Options, Sensor settings and adjust the volume scale to ensure the volume can be read off the axis when the line is extended to 100 C and 0 C. 3. Print the graph out. 4. Use a ruler to draw a best fit line to extend the line forwards to 100 C and backwards to 0 C. 5. Read off the volumes of the gas at 0 C and 100 C. 6. Add the volume of the apparatus to the 0 C and 100 C readings and find the volume increase from 0 C to 100 C. he calculation Charles law uses; he volume at 100 C he volume at 0 C he Change in volume, from 0 C to 100 C he change in temperature. For the calculation the temperature is assumed to have risen by 100 C. he volume of the apparatus at 0 C and 100 C are derived from the printed and extrapolated graph. Substitute the values and solve; (volume at 0 C x 100) (Change in volume 0 C to 100 C) = Absolute Zero You will have to place the negative in front of the number. Calculating Absolute Zero using the graph Draw a best fit line on the graph of otal olume vs. emperature. Right click on the screen and select Zoom In. Use Zoom so that the graph occupies most of the screen (2)

4 Use ools, Best Fit, select Manual, select Y-Axis = otal olume and X-Axis = emperature, select OK. Click at one end of the straight section and drag the pointer to the other, and release the mouse button. he Best Fit line is displayed and the equation of the line is shown in the form:- y = mx +c. Using the Best Fit line equation he equation for the best fit line is of the form:- y = mx + c Substitute and t for y and x. he equation becomes: = mt + c You require the value of t for zero volume: Solving for t: 0 = mt +c t = -c m Substitute in the values of c and m (the gradient) from the Best Fit line equation, and calculate t. Manually extrapolating the graph Right click on the screen and click on Zoom Off In the Display menu select Sensor Settings, double click on the Min emperature, and change the value to minus 300, click on OK. You should get a graph like the one below:- Print the graph and, using a ruler, extrapolate the Best Fit line until it crosses the emperature axis. he value where it crosses the emperature axis is the measured value for the Absolute Zero of temperature (2)

5 Charles law he accepted value for the Absolute Zero is -273 C. On the Kelvin scale of temperature, absolute Zero = 0K. herefore 0 º C = 273K Charles Law states: he olume of a fixed mass of gas is directly proportional to the emperature in Kelvin as long as the pressure remains constant. = k he Law can be usefully expressed as follows:- 1 = Questions Draw a sketch of a graph of olume vs. emp for a gas, if the temperature is in Kelvin. here are 5 litres of air, at a temperature of 300 K, enclosed in a cylinder with a piston that is free to move. he temperature is raised to 400 K, while the pressure remains the same, and the piston moves out. What is the new volume of air? 1. What are the sources of error in this investigation? 2. How could you control the investigation to reduce the errors? 15-5 (2)