In this experiment students will measure of the volume of a fixed quantity of a gas as the pressure exerted on the gas is varied at constant temperature. Students will attempt to verify Boyle’s law. They then will measure of the volume of a fixed quantity of a gas as the temperature is varied at constant pressure. Students will attempt to verify Charles's law. Students will make these measurements by analyzing videotaped experiments.
The ideal gas law states that for a fixed volume of an ideal gas (PV/T) = nR = constant. Here P and V are the pressure and volume of the gas at absolute temperature T. (See class notes.) Theoretical derivations of the ideal gas law neglect the forces that the gas molecules exert on each other. Real gases therefore do not strictly obey the ideal gas law. However, at sufficiently low densities, intermolecular forces do not play a significant role and the ideal gas law becomes increasingly accurate. For instance, at 20 atm pressure and room temperature, the volume of 1 mole of oxygen gas is about 2.3% smaller than predicted by the ideal gas law, but at 1 atm pressure the volume is only about 0.13% smaller.
If the temperature T is constant the ideal gas law yields Boyle’s law, PV = constant (at constant T). If the pressure is held constant, the ideal gas law yields Charles's law, V/T = constant (at constant P).
The PASCO TD-8572 Heat Engine/Gas Law Apparatus is used for the measurements. The heart of this apparatus is a nearly friction-free piston-cylinder system. The graphite piston fits snugly into a precision-ground Pyrex cylinder so that the system produces almost friction-free motion and negligible leakage.
The Heat Engine/Gas Law Apparatus is designed with two pressure ports with quick-connect fittings for connecting to an air chamber or to a pressure sensor with tubing.
The apparatus includes the following equipment:
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base apparatus
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air chamber | ||||||
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3 hose configurations:
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1 one-holed and 1 two-holed rubber stopper |
Part 1: Boyle's law
At constant temperature, the gas in the cylinder is compressed. A pressure sensor measures the pressure with respect to some reference pressure. You will find the volume of the gas in the cylinder as a function of pressure by stepping frame-by-frame through a video clip.
To play the video clip or to step through it frame-by-frame click the "Begin" button. The "Video Analysis" web page will open. You can toggle between the current page and the "Video Analysis" page by pressing Alt-Tab. Choose one of the gas_1.avi video clips.
| Play the video clip. When finished, the video clip will rewind automatically and stop at frame 0. | ||||||||||
| Open a new spreadsheet in Microsoft Excel. | ||||||||||
| Step through the video clip frame-by-frame and record the pressure and the
volume of the gas in the cylinder for each frame in the spreadsheet.
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| Boyle’s law states PV = constant, or P = constant / V. In this experiment P = Pdisplayed + P0, where P0 is the reference pressure of the pressure sensor. Therefore Pdisplayed = constant / V - P0. A plot of Pdisplayed versus 1/V should yield a straight line. If it does, you have verified Boyle’s Law. Produce a graph of Pdisplayed versus 1/V as described in a previous exercise. | ||||||||||
| On the menu bar click tools, data analysis, regression. For the input y range choose column containing Pdisplayed. For the input x range choose the corresponding cells of the column 1/V. Under output options check new worksheet, and under residuals choose line fit plots. Click OK. | ||||||||||
| The regression function finds the best fitting straight line for your data. Under SUMMARY OUTPUT, X Variable, you will find the slope of this line, and the standard error in this slope from the fit. |
Part 2: Charles's law
At constant pressure, the temperature of the gas in the cylinder and air chamber is varied. The air chamber is placed in a container with water at room temperature, and then ice is added to the water. A temperature sensor measures the temperature of the water. You will find the volume of the gas in the cylinder as a function of the temperature by stepping frame-by-frame through a video clip.
To play the video clip or to step through it frame-by-frame click the "Begin" button. The "Video Analysis" web page will open. You can toggle between the current page and the "Video Analysis" page by pressing Alt-Tab. Choose one of the gas_2.avi video clips.
| Play the video clip. When finished, the video clip will rewind automatically and stop at frame 0. |
| Step through the video clip frame-by-frame and record the temperature T and the
volume of the gas in the cylinder for each frame in your spreadsheet.
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| Charles's law states V = constant ´ T,
where T is the absolute temperature. In this experiment V = Vdisplayed + V0, where V0 is the volume of the air chamber, and T(K) = T(oC) + 273. Therefore Vdisplayed = constant ´ T(oC) + constant ´ 273 - V0. A plot of Vdisplayed versus T should yield a straight line. If it does, you have verified Charles's Law. Produce a graph of Vdisplayed versus T(oC). | ||||||||
| On the menu bar click tools, data analysis, regression. For the input y range choose the column containing Vdisplayed. For the input x range choose the corresponding cells of the column column containing T (oC). Under output options check new worksheet, and under residuals choose line fit plots. Click OK. | ||||||||
| The regression function finds the best fitting straight line for your data. Under SUMMARY OUTPUT, X Variable, you will find the slope of this line, and the standard error in this slope from the fit. |
Open Microsoft Word and prepare a report using the template shown below.
| In a few sentences summarize the experiment. |
| Show your spreadsheet entries from part I and part II. |
| Answer
the following questions:
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Save
your Word document (your name_lab2.doc) and attach it to an e-mail message to mbreinig@utk.edu.
