Ideal Gas Law EX-9950Page 1 of 8

Ideal Gas Law EX-9950Page 1 of 8

Ideal Gas Law

EQUIPMENT

INTRODUCTION

The temperature, volume, and pressure of a gas are measured simultaneously to show that they change according to the Ideal Gas Law. Special cases of constant volume, constant temperature, and adiabatic are also investigated.

THEORY

In 1662, Robert Boyle discovered that the product of the pressure (P) and volume (V) of a gas at a constant temperature is constant.

PV = k1

Where, k1 is a constant.

Therefore, the pressure and volume are inversely proportional.

In the 1787, Jacques Charles experimentally verified that the volume and temperature (T) of a gas at constant pressure are directly proportional.

V=Tk2

Where, k2 is a constant.

In 1802, Joseph Gay-Lussac discovered the direct relationship between the pressure and temperature of a gas at constant volume:

P=Tk3

Where, k3 is a constant.

The Ideal Gas Law combines the three discoveries above. It relates the absolute pressure (P) and volume (V) of a gas to the absolute temperature (T) in degrees Kelvin.

PV=nRT

where n is the number of moles of gas, and R is the ideal gas constant.

Part I: Ideal Gas Law Syringe

SETUP

The Ideal Gas Law Syringe allows simultaneous measurements of temperature and pressure of a gas as it is compressed. The mini stereo jack is connected to a low thermal mass thermistor built into the end of the syringe to measure temperature changes inside the syringe. The mini stereo jack plugs directly into the temperature sensor.

The white plastic tubing coupler attaches to the port of the pressure sensor: A slight twisting motion locks the coupler onto the port. This white plasticconnector can be disconnected and re-connected during the experiment to allow for different initial plunger positions. All of the clear plastic fittings are glued in place and cannot be removed.

The plunger is equipped with a mechanical stop that protects the thermistor, and also allows for a quick, predetermined change in volume. Never slam the plunger down on the table. Always grip the syringe and plunger as shown to compress the air.

PROCEDURE

1.In DataStudio, construct a graph of Pressure (kPa) vs. Time and Temperature (K) vs. Time. Set the sample rate to 20 Hz.

2.Disconnect the white plasticpressure coupler from the pressure sensor. Press the plunger of the syringe all the way in until the handle of the plunger bottoms out on the mechanical stop. Record this minimum volume: It should be close to 20 cc.

3.Set the plunger at 40 cc, and then re-connect the coupler to the sensor.

4.Start recording data. Quickly compress the plunger all the way in, and keep it compressed. The plunger handle should be bottomed out against the mechanical stop.

5.Watch the graphs of pressure and temperature, and continue to hold the plunger in until the values are no longer changing. This should take around 10 seconds.

6.After the temperature and pressure have equalized, release the plunger. Again, watch the graphs and wait until the values are no longer changing.

7.Stop data collection.

ANALYSIS

1.Look at your pressure and temperature graphs. Correlate the changes in pressure and temperature to the movement of the plunger.

2.What happened to the temperature when the air was compressed? Why?

3.What is the equilibrium temperature of the gas when it was compressed? Why? What is the equilibrium pressure? Why does it not go back to “roompressure”?

4.What happened to the temperature during the expansion (when you released the plunger)? Why? Does it go below room temperature? Does the pressure go below “room pressure”? What would you have to do to make this happen?

5.Create a Data Table in DataStudio of the Pressure and Temperature data.

6.Measure the initial temperature (T1) and pressure (P1)of the gas from your data just before you compressed it. You can highlight an area (click and drag) in the graph and that data will appear in the data table. This data corresponds to an initial volume (V1) of 40cc.

7.Highlight the area on the temperature graph where it peaks. Pick the place where the temperature has peaked, not the pressure. It takes the temperature sensor about 1/2 second to respond. Record the peak temperature (T2) and the corresponding pressure (P2) for that time. You want two values that occurred at the same time. This data corresponds to the volume (V2) of 20cc. Note: If the compressed volume marked on the syringe is different than 20 cc, use that value instead.

8.Use the Ideal Gas Law to show that the ratio of volumes can be expressed as

where the subscript 1 refers to the initial state (volume = 40 cc) and the subscript 2 refers to the final state (volume = 20 cc) after compression.

9.Use your values of pressure and temperature to calculate the ratio of volumes. How does this compare to the actual ratio? Are they about the same?

Part II: Constant Temperature

PROCEDURE

1.Add a digits display of temperature in DataStudio.

2.Disconnect the white plastic coupler from thepressure sensor. Set the plunger at 45 cc, and then re-connect the coupler to the sensor.

3.Start recording data. Compress the plunger to 40 cc and hold it at this position. Watch the temperature on the digits display and wait until it has dropped down to close to room temperature. Note the final temperature. Each time you compress the air in this sequence, wait until the temperature returns back down close to this value.

4.Compress the plunger to 35 cc and hold it at this position. Watch the temperature, and hold the plunger at 35 cc until the temperature has dropped to the value you noted in step 3. Do not release the plunger.

5.Compress the plunger to 30 cc, and wait until the temperature drops as before.

6.Repeat for 25 cc and 20 cc.

7.Stop recording data.

ANALYSIS

1.Look at your pressure and temperature graphs. Correlate the changes in pressure and temperature to the movement of the plunger.

2.Highlight the area on the graph when the plunger was at 40 cc. Use the data table to determine the equilibrium pressure and temperature.

3.Repeat for all other volumes. For each position, pick the pressure that has the temperature closest to the “equilibrium” value. It does not matter what this temperature is, as long as all pressures are measured at the same temperature. Record all your values in a table.

4.For each of the pressures, calculate the inverse pressure (1/P). Graph Volume vs 1/P. Why does this give a straight line? Use the Ideal gas law to show that a graph of Volume vs 1/P results in a straight line with a slope given by

Slope = nRT

5.Determine the slope of this line from your graph of Volume vs. 1/P. Use your values to determine the number of moles (n) of air in the syringe. Pay attention to the units!

6.Look carefully at the graph. Why is there an offset in the axis for the volume? How do you account for this extra volume?

FURTHER INVESTIGATIONS

1.Disconnect the white plastic coupler from the pressure sensor. Set the plunger at 60 cc, and then re-connect the coupler to the sensor.

2.Repeat the procedure, taking pressure and temperature data at each of the volumes (40cc, 35cc, etc.) as you did before.

3.Put this new data on the same graph. Why is this slope different? Is the volume offset about the same as before?

Part III: Adiabatic Compression

PROCEDURE

1Set the sample rate at 50 Hz

2.Disconnect the white plastic coupler from thepressure sensor. Set the plunger at 60 cc, and then re-connect the coupler to the sensor.

3.Start recording data. As quickly as possible, compress the plunger from 60 cc down to 20 cc. Do this in one quick motion, bottoming out the piston on the mechanical stop.

4.Stop recording data.

ANALYSIS

1.Measure the initial temperature (T1) and pressure (P1)of the gas from your data just before you compressed it. This data corresponds to an initial volume (V1) of60cc.

2.For an adiabatic compression, the initial pressure and volume (P1, V1) are related to the final pressure and volume (P2, V2) by

where (gamma) is the ratio of specific heats, and for air has a value of 1.40. Use your values to calculate the theoretical peak pressure if the compression was adiabatic.

3.Measure the peak pressure (P2) after compression. Was this truly adiabatic?

4.Using the Ideal Gas Law, calculate the theoretical peak temperature.

5.Measure the peak temperature after compression. Why did it not occur at the same time as the peak pressure? Why is this temperature so much lower than the theoretical?

Part IV: Constant Volume

SETUP

The Absolute Zero Apparatus consists of a hollow sphere that acts as a container of constant volume as the apparatus is placed in different temperature water baths. Plug the mini stereo jack into the temperature sensor to measure the temperature using the thermistor imbedded in the wall of the sphere. Connect the white plastic coupling to the port of the pressure sensor to measure the pressure inside the sphere.

You will need a source of hot water and a source of cold water (or ice).

PROCEDURE

1.Use the calculator in DataStudio to calculate absolute temperature in degrees Kelvin. Set up a graph in DataStudio of pressure vs. absolute temperature.

2.Set the sample rate at 10 Hz . Select Manual Sampling from the sampling options in the Setup menu. It is also helpful to set up digit displays of temperature and pressure.

3.Fill one of the plastic containers with enough hot water to cover the sphere. Use the other container for a supply of cold water (or ice). Make sure the white plastic coupler is connected to the pressure sensor before putting the sphere in the hot water.

4.Start data collection. Completely submerge the sphere and wait for the pressure and temperature to equalize. Click on keep in the top menu bar to save that data pair.

5.Add cold water (or ice) to decrease the temperature of the water 5 to 10 degrees. Stir the water to get an even temperature and click on keep when the pressure and temperature equalize.

6.Keep decreasing the temperature and taking data until you have the system as cold as you can get it. You may need to dump out some of your water.

ANALYSIS

1.Use calipers to measure the diameter of the sphere, and calculate its volume. Is this measurement more or less than the actual volume of the sphere? Why?

2.Use the Ideal Gas Law to show that a graph of Pressure vs. Temperature results in a straight line with a slope given by:

3.Determine the slope of this line from the Pressure vs. Temperature graph. Use your values to determine the number of moles (n) of air in the sphere. Pay attention to the units!

FURTHER INVESTIGATIONS

1.Re-fill the container with hot water.

2.Disconnect the white plastic coupler from the pressure sensor and place the sphere in the hot water. Does air flow in or out of the sphere? Re-connect the coupler to the sensor.

3.Repeat the procedure, taking pressure data at different temperatures as you did before.

4.Put this new data on the same graph. Why is this slope different? Calculate the new number of moles of air.

CONCLUSION

1. Describe what happens to the pressure of a gas at constant temperature when its volume is changed.

2. Describe what happens to the volume of a gas at constant pressure when its temperature is changed.

3. Describe what happens to the temperature of a gas at constant volume when its pressure is changed.

Written by Jon Hanks