lecdem.physics.umd.edu - Kinetic and Diffusive Processes

Kinetic and Diffusive Processes

I3-03: GALILEO'S THERMOSCOPE

I3-03

Measure very small pressure changes.

Without touching the can, disconnect and reconnect the tubing from the Magnahelic gauge in order to set the gauge pressure to zero. Warming the can by placing your hand on it raises the pressure in the can about half of the full scale. Also try warming the can by breathing on it.

I3
I3-04: GALILEAN THERMOMETER

I3-04

Illustrate a very heat-sensitive device.

This air thermoscope consists of a flask sealed with a stopper with a 4 mm diameter 50 cm long glass tube inserted into the (colored) water bath in the bottom of the flask such that the water level in the tube is at the level of the water in the flask. The water level in the tube rises when the flask is warmed by snuggling it in your hands.

I3
I3-31: IDEAL GAS LAW - VOLUME OF ONE MOLE

I3-31

Demonstrate that one mole of gas occupies 22.4 liters at STP.

Pour liquid nitrogen into the small beaker and let it boil down to about 35 ml. The density of liquid nitrogen is 0.808 g/ml, so one mole has a mass of 28 grams and occupies about 35 ml. Install the neck of the balloon over the beaker, and allow the liquid nitrogen to evaporate, filling the balloon. Determine the average circumference of the balloon and from that calculate the diameter. The approximate volume of one mole of nitrogen gas at atmospheric pressure is then V= 4 pi r3/3, which can be readily calculated. This determination is good to better than ten percent.

I3, I0
I3-33 HELIUM BALLOON ON LIQUID NITROGEN

I3-33

Demonstrates how a gas contracts when cooled

A helium balloon which is cooled by resting on a liquid nitrogen bath becomes becomes more dense -- by about a factor of 4. When the balloon is removed from the liquid nitrogen it warms up, expands, and floats away, unless it is tethered

I0, FS1
I3-41: BOYLE'S LAW - PROJECTION

I3-41

Demonstrate Boyle's law.

Connect the piston tube to the pressure gauge. Read off several values of pressure and volume for different piston positions to show that PV=constant.

I3
I3-42: BOYLED MARSHMALLOWS

I3-42

Amusing demonstration of Boyle's Law.

A marshmallow is placed in a bell jar. As the air is pumped out of the jar the pressure inside becomes smaller and the little bubbles of air in the marshmallow increase in size, inflating the marshmallow. Eventually much of the air originally in the marshmallow is pumped away. When the air is let back in, atmospheric pressure compresses the marshmallow to a small fraction of its original size.

An alternative demonstration uses a balloon with a small amount of air in it in place of the marshmallow. The photographs above show the marshmallow: before pumping, after pumping, and after the air is let back into the bell jar, and the balloon: before pumping and after pumping.

Please bring own marshmallow.

I3, FS1
I3-51 CHARLES' LAW - PROJECTION

I3-51

Demonstrates Charles' law

A hollow sphere filled with air is connected by a tube to a pressure gauge on an overhead projector. Place the sphere in ice water (T=273K) and in boiling water (T=373K), and read the pressure for each as well as at room temperature.

I3, I0
I3-52: CONSTANT VOLUME GAS THERMOMETER - ABSOLUTE ZERO

I3-52

Determine the value of absolute zero.

With a constant volume of air in the chamber, measure the pressure P(B) at the boiling point and the pressure P(F) at the freezing point of water. If the pressure P is read at some arbitrary temperature T, then that temperature in degrees celsius is:

T=100 [P-P(F)] / [P(B)-P(F)]

For an ideal gas, the pressure should go to zero at the temperature of absolute zero. Setting P=0, the value of absolute zero in degrees celcius can be calculated.

Another way to do this is to plot a graph of pressure as a function of temperature. Draw the best line through the three points determined at boiling, freezing, and room temperature, and extend it so that it intersects the pressure axis, which is T=0 in celsius degrees.

Above are photographs of the pressure gauge at each of the three points described.

I3, I0
I4-17: AIR BALLOON ON LIQUID NITROGEN

I4-17

Demonstrate dramatically that the volume of vapor is greater than the volume of the same amount of liquid.

An air balloon is held on top of a liquid nitrogen bath. The volume of the air balloon decreases for two reasons: first, the volume of the gas shrinks according to Charles' law, and second, some of the air changes to liquid and shrinks considerably. Liquid nitrogen will readily cause oxygen to liquify, and even liquify some of the nitrogen in the balloon.

I0
I4-52: CARBON DIOXIDE BALLOON ON LIQUID NITROGEN

I4-52

Demonstrate condensation sublimation.

A balloon filled with carbon dioxide gas is held on top of a liquid nitrogen bath. The volume of the balloon decreases for two reasons: (1) the volume of the gas shrinks according to Charles' law, and (2) the boiling point of carbon dioxide is well above that of nitrogen, so the carbon dioxide condenses, forming dry ice powder. The small granules of dry ice, which can be easily seen in the deflated balloon, disappear as the balloon warms up and inflates once again.
I5-22 FIRE SYRINGE

I5-22

Demonstrates heating air by compression

This demonstration consists of a transparent cylinder with a flared base, and a plunger that can be pushed into it. A small (very small) piece of cotton is pushed into the bottom of the tube using the wire provided, and the plunger is sealed into the tube. The plunger is pushed down sharply, compressing and thereby heating the air within. The temperature rises high enough to ignite the cotton with a flash, which can be readily seen through the plastic tube.
Engagement Suggestion
• Consider inviting a volunteer from the audience to try the demonstration. This will require careful supervision, but is safe. Just ensure that the syringe isn't knocked off the table by an overenthusiastic student!
• This demonstration works best with a very small amount of cotton to ignite, no more than a few millimeters at most. Consider showing the device with different amounts of cotton, and how the results change. Encourage students to discuss reasons for this.

Background
This demonstration illustrates that an essentially fixed mass of air will increase in temperature when its volume is reduced, i.e. it is heated when compressed. The fire syringe is a simple piston, and can be used to introduce a discussion of the use of pistons in engines.
Consider using this demonstration in conjunction with both other thermodynamics demonstrations from section I5, and relating it back to general gas behaviour with demonstrations from section I3.

I5
I6-01 GAS PRESSURE - MODEL

I6-01

Illustrates the molecular nature of gas pressure

A vibrator motor is activated causing chaotic motion of a group of ball bearings in a clear plastic container. The upward motion of the ball bearings pushes a black plastic plate upward, indicating the upward force of "air pressure" on the plate. Increasing the speed of the motor by turning up the variac increases the average speed of the balls and pushes the plate up further, modeling a greater pressure.

I6, PW1
I6-02: NITROGEN DIAMETER AND MEAN FREE PATH

I6-02

Experimentally determine the diameter of the nitrogen molecule and to determine the order of magnitude of the mean free path of nitrogen gas molecules at STP.

Using the pan balance pour 700 cm3 of liquid nitrogen and demonstrate that it has a mass of about 560 grams. The mass of the dewar is about 421 grams. For liquid nitrogen the volume per molecule can then be determined to be

Vol/Mol=700 cm3/[(560g)/(28g/mole)(1mole/6.0x1023molecules)]=5.8x10-23cm3.

Assume molecule is a cube, so d = 3.9x10-8 cm.

Volume per molecule @ STP = 22.4x103 cm3 / 6.0 x 1023 = 3.7x10-20 cm3

Mean free path = V/d2 = 3.7x10-20 cm3 / (3.9x10-8 cm)2 = 2x10-5 cm.

I6, I0, ME1
I6-03 EQUIPARTITION OF ENERGY

I6-03

Demonstrates equipartition of energy

Into the glass bowl are placed balls of the same size but three different masses: ping pong balls, cork balls, and superballs. Shaking the bowl gives all of the balls approximately the same kinetic energy. Because the light balls have greater velocities for the same average kinetic energy, as you shake the bowl more and more fervently first the ping pong balls, then the cork balls, and finally the superballs jump out.

I6
I6-11: BROWNIAN MOTION WITH TV

I6-11

Demonstrate Brownian motion.

A smoke cell is mounted on a tube connected to a TV camera. On the end of the tube inside the cell is a microscope lens which casts an image of smoke particles in the cell onto the videcon of the TV camera. The focal plane of the microscope/TV system is illuminated by a laser to avoid creation of convection currents by heating with a more powerful light source. A twisted lab tissue is burned and blown out, and while it is smoking the rubber bulb on top of the smoke cell is used to snort smoke into the cell through a tube in the bottom of the cell. After a few seconds convection ceases and Brownian motion is clearly visible on the TV monitor to large groups. The photographs above show the entire system (left), the laser beam entering the smoke cell which is in turn mounted on the video camera (center), and the output of the video camera sent directly to the video frame grabber used to capture the images (right). Clicking on the link below will play a 30 second MPEG movie of the particles in motion.
I6-13: AIR TABLE - MODEL OF BROWNIAN MOTION

I6-13

Simple model of Brownian motion.

The small pucks represent air molecules, which chaotically strike the larger smoke particle, producing irregular motion of the smoke particle. Be careful with this model, however: in reality, because of the enormous size of a smoke particle relative to the size of an air molecule, it takes a net of about 10^4 molecules of air on one side relative to the other side of the smoke particle to make it change its motion noticeably. Many people overlook the statistical basis of Brownian motion, and believe incorrectly that a single molecule of air might be able to noticeably change the motion of a smoke particle.
Note: The air table is only available in rooms 1410, 1412, and 0405 because it will not fit through a standard door.
I6-21 GAS DIFFUSION - MODEL

I6-21

Models gas diffusion through a small hole

A large chamber has been divided by a plastic barrier. A mechanical shaker allows the chamber to be vibrated. We place balls of different colors on either side of the barrier. When the chamber is shaken, the balls bounce around like particles in a gas. The barrier dividing the chamber can be slid out partially or entirely, allowing a small opening or a complete merger of the sections.
Engagement Suggestions
• Encourage students to predict what will happen when the barrier is opened.
• Once the students have made predictions and seen the results, ask if this process is reversible. Could the balls ever all return to their original sides? (Compare I6-52.)

Background
This device models gas diffusion through an opening. As the two “gases” mix, the balls from either side move to the other, and eventually are evenly distributed on both sides.
I6-22: IODINE DIFFUSION TUBES

I6-22

Demonstrate diffusion.

Two tubes are presented, both having a small amount of iodine crystals in the end. However, one contains air at a low pressure and the other contains air at near atmospheric pressure. When the iodine is heated, the difference in diffusion rate of the iodine through the two tubes is readily apparent.
I6-23 DIFFUSION - FOOD COLOR IN WATER

I6-23

Demonstrates diffusion

A drop of food coloring is placed gently into a beaker of water. In a few minutes the food coloring will diffuse through the entire beaker of water.

F2, glassware
I6-24: DIFFUSION VELOCITY

I6-24

Show that the diffusion velocity is proportional to the RMS molecular velocity.

Cotton swabs dipped into HCl and NH4OH respectively are inserted into the ends of the tube. HCl gas (molecular weight 36.5) and NH3 or ammonia gas (molecular weight 17) begin to diffuse inward. In less than 25 minutes they meet, forming a ring of ammonium chloride (NH4Cl). The diffusion velocity is proportional inversely to the square root of the molecular mass, because according to equipartition of energy the average molecular speed is inversely proportional to the square root of the molecular mass. This means that the distances traveled by each vapor before they meet are in the proportion:
d(NH3):d(HCl)=SQRT(36.5/17)=3:2 approximately.

Use caution when handling chemicals. Always wear protective gloves. Please do not throw used swabs in garbage; place in included water beaker instead for proper disposal.