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Lab 7 Gases

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Lab 7 Gases

Lab 9: Gases Physics 193 Fall 2006

    Lab 9: Gases

I. Introduction

Today’s lab involves so-called gas lawsrelationships between quantities that are used

    to describe fluids such as air. We will confirm several such relationships:

    ? A relationship between the pressure and temperature of a fixed volume and amount of

    air.

    ? Qualitative and quantitative relationships between the pressure and volume of a gas at

    constant temperature and with a constant amount of air.

    Relationships such as these are useful for analyzing conditions in the atmosphere, the

    operation of a hydraulic lift, and how engines work.

II. Theory

    Gases are described by so-called macroscopic quantities: pressure P, temperature T, volume V, and the amount of substance (n moles or N particles). The latter two, volume

    and the amount of substance, are often combined in the quantity density ???

    ? The pressure P of a fluid (such as air) against a surface is the force F that the fluid

    exerts perpendicular to a surface of area A divided by that area: P = F/A. Pressure is

    2measured in the metric system in pascals where 1 Pa = 1 N/m. Many everyday

    pressure measuring devices give pressure in mmHg where 1 mmHg = 760 Pa.

    ? Temperature T is measured using a thermometer of some type and depends on the

    average random kinetic energy per molecule of that substancethe hotter the

    substance, the greater the random kinetic energy of its atoms and molecules.

    oTemperature is measured in degrees celsius (C) or in kelvins (K). 3? Volume V is the amount of space that the fluid occupies and is measured in m.

    ? The amount of the fluid is given either as the number of moles n of the substance or

    the number N of particles of the substance. 1 mole is the number of particles of that

    substance that are contained in an atomic or molecular mass of the substance in units

    of grams. For example, 1 mole of molecular hydrogen gas H would be 2.0 g, 1 mole 2

    of molecular oxygen gas O would be 32 g. The mole and the number do not have 2

    units.

How are these quantities related? Today we will confirm two relationships:

? Isochoric process: If the amount of gas and the volume of the gas are constant, then

    the pressure in the gas is proportional to the temperature of the gas:

    P = Constant T, for constant V and n or N.

? Isothermal process: If the temperature and the amount of the gas are constant, then

    the pressure in the gas is inversely proportional to the volume of the gas:

    P = Constant/V, for constant T and n or N.

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Lab 9: Gases Physics 193 Fall 2006

    III. Experiment 1: Relating the pressure and temperature of air

    Equipment: Thermometer, a pressure gauge, a hot plate, some ice in a container with water, and a stirrer.

    Experiment: You have a sealed hollow metal sphere with air inside and a pressure gauge on top. You will vary the temperature of the gas inside the sphere and measure the

    corresponding air pressure inside the sphere using the gauge on the top of the sphere. To

    vary the temperature, the metal sphere can be submerged in an aluminum container of

    water such that the water provides a temperature bath for the sphere and its contents. By

    appropriate use of ice cubes and the hot plate, you can vary the temperature of the bath

    over a range of temperatures. Make sure that only the aluminum bucket that holds the

    water goes on top of the hot plate, and that the metal sphere does not touch the walls of

    the aluminum water container when it is on the hot plate.

    Problem: Your ultimate goal for this experiment is to confirm the relationship between the pressure and temperature of the air that was described in the theory sectionthat is,

    when the volume and the amount of gas are kept constant.

Procedure: Here is what you will need to do.

a) Fill the aluminum container about half full with ice-water slush. The slush should be

    about two-thirds water and the rest ice. Stir the slush so it becomes a uniform

    temperaturethe freezing temperature of water or about 0

    oC. (It may stabilize a little oabove 0 Crecord this lowest temperature.) b) Place the sphere completely inside the ice-water slush. Be sure the sphere does not

    touch the sides of the aluminum pail. If the slush does not completely cover the sphere,

    add a little extra water and ice. The pressure gage should be sticking out of the slush so

    that you can read it.

c) Before putting the sphere in the slush, it had been at room temperature. When placed in

    the slush, it will transfer thermal energy to the water and ice that contact the metal sphere.

    Thus, you should continue to stir the slush so that the approximately 0 oC ice water is ocontinually contacting its surface. This will cool the sphere to about 0 C. To be sure it is

    near this low starting temperature, stir the slush with the sphere in it for about 5 minutes.

    The pressure reading should stabilize when the temperature of the air inside has stabilized

    oat about 0 C.

     oC) Pressure (Pa_) Temperature (d) Record this pressure and the corresponding otemperatureabout 0 C in the data table at the right, or you own table in your lab notebook. e) You now need pressure readings for other temperatures. Turn on the hot plate. It will first warm the ice water slush so that the ice all melts

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    oC. Continue gently stirring the slush so that it stays Lab 9: Gases Physics 193 Fall 2006 at a uniform temperature as the ice in the slush melts and then when all of the ice has

    melted, the liquid bath starts to warm.

     still at its lowest temperature near 0

    f)Take temperature and pressure readings about every two minutes. Go from the low

    ostarting temperature to about 70-80 C. Record the readings in the data table.

g) You want next to make a graph of pressure (the dependent variable)-versus-

    temperature (the independent variable). Enter your data in Excel or Graphical Analysis

    software. It should look like a linear function, that is, pressure increases as temperature

    increases. Use the software to get a best-fit function for your data. Remember to show the

    equation and the R2 value of your best fit on the graph. (The R2 value tells you how good

    the fit is a perfect fit has a R2 value of 1.)

h) Print your graph. We would like to use it to determine the lowest temperature the gas

    could reacha temperature where the air pressure would be zero. Use the equation you

    found in g) to predict the value of the temperature when the pressure is zero. Also,

    carefully extend the pressure-versus-graph line back to find the place where it crosses the

    horizontal temperature axis. This crossing point is the place where the pressure would be

    zero and should be similar to the answer for the lowest possible temperature reached as

    determined using the equation. You have predicted the value of the lowest temperature

    to which you can cool this gas. This temperature is called absolute zero on the Kelvin

    temperature scale.

IV. Experiment 2: Quantitatively relate the pressure and volume of air

Experiment: Consider the following experiment by Thandi. She used a large cylindrical

    syringe whose radius was measured to be 2.0 cm and was about 30 cm long. She set the

    plunger so that the column of air in the tube was 15 cm long and then attached a pressure

    gauge to the other end, sealing the air in the tube so that it could not escape. A schematic

    diagram of the apparatus is shown below.

Problem: Your objective is to confirm the quantitative relationship between the varying

    pressure exerted on a gas and the variation in the volume of space (the volume) of the gas.

    The relationship is known as Boyle’s law.

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Lab 9: Gases Physics 193 Fall 2006

    Procedure: Thandi slowly decompressed and compressed the air in the tube by pulling and pushing the plunger out and in, carefully noting the volume of the column of air and

    the reading on the pressure gauge. Here is what you will need to do.

     3 = ml) a) Determine the volume of the air column and the corresponding pressure reading for a Pressure gauge Volume of air in variety of volumes bigger and smaller than reading (Pa) (cm the starting volume. Enter the data in the table at the right. b) Open either Excel or Graphical Analysis software graph of pressure-versus-volume for the gas. Consider the pressure as the dependent variable that changes as you changed the volume of the gas. Volume is

    then the independent variable. Enter the data

    into whichever software you are using.

c) Try fitting various best-fit curves to the data using the ―Add trendline‖ function in

    Excel, or the ―Curve Fit‖ function in Graphical Analysis. In each case, remember to show 2 value on the graph. (The R2 value tells you how good the fit is a the equation and the Rperfect fit has a R2 value of 1.0.)

d) Which curve fits the data best?

e) There are other curves that are very close to being the best-fit curve. Can you eliminate

    any of these candidate curves by appealing to intuitive reasoning? To do so, try asking

    the following questions.

    I. Is it possible to have a negative pressure or a negative volume? Explain why or

    why not. Does that help eliminate any of the curves?

    II. Consider two limiting cases. If you let the volume become very large, what

    should happen to the pressure of the gas? If you force the volume to become very

    small, what should happen to the pressure? Does this help you eliminate any of

    the curves? Explain.

f) Formulate a mathematical relationship between the pressure and volume of air.

    Is the relationship consistent with Boyle’s law?

V. Experiment 3: Qualitatively relate the pressure and volume of air

    Equipment: Long narrow tube, putty, graduated cylinder filled with water, and meter stick.

    Experiment: Seal one end of the tube using putty. With the tube oriented vertically, slowly lower the open end of the tube into the graduated cylinder filled with water. The

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    Lab 9: Gases Physics 193 Fall 2006

    pressure on the air inside the tube increases as the open end of the tube is lowered deeper

    into the fluid. You will see water slowly enter the bottom of the tube as the open end gets

    deeper in the water. This water entering the bottom of the tube decreases the volume of

    the air inside the tube. Thus, you should be able to qualitatively observe that the

    increasing pressure with increasing depth in the water causes the decreasing volume of

    the air. The procedure below will help you more clearly observe this phenomenon.

    Problem: Your objective is to observe that the increasing pressure causes the volume of

    air to decrease in agreement with the behavior of an isothermal gas process.

    Procedure: Here is what you will need to do.

    a) Place a small piece of putty in the end of the glass tube

    b) Fill the graduated cylinder with water to about 5 cm from the top of the cylinder.

    c) Hold the glass tube vertical with the closed end (the putty end) on top and the open end

    on bottom.

    d) Slowly lower the open end so that it is slightly below the surface of the water. You

    now have a confined amount of air in the tubethe volume of the air can change but the

    amount of air (the number of moles or the number of air particles) is constant.

    e) Now lower the open end about 10 centimeters deeper into the water. We will use

    Pascal’s law to estimate the pressure at some depth h in the water compared to the

    atmospheric pressure at the water’s surface:

    P = P

     + ? g h, atmosphericwhere ? is the density of the water and h is the distance below the surface of the lowest part of the air in the tube. The pressure of the water against the air at the bottom surface

    of the air column is now ? g h greater than at the surface. Notice that a small amount of water has entered the bottom of the glass tube. Consequently, the volume of the air is less

    than it was when at the surface.

f) Lower the open end farther into the water so the bottom end is about 20 cm below the

    surface. Is the pressure that the water exerts on the bottom of the air in the tube now

    greater, less than, or the same as before? Did the air volume decrease or increase? Are

    these changes consistent with Boyle’s law?

g) Move the end of the rod with the air in it deeper into the water. Are any changes that

    you observe consistent with Boyle’s law? Explain.

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Lab 9: Gases Physics 193 Fall 2006

     VI. Homework

    In Lab X, you will do experiments involving thermodynamics. The following problem

    will help you prepare for that lab. Please solve the problem before coming to lab and

    bring the solution to turn in at the beginning of the lab.

1. If you drink cold water, it will soon warm to your body temperature (about 37?C). The

    water acquires thermal energy from your body. Therefore, you ought to be able to control

    your weight by drinking lots of cold water. Estimate the volume of cold water you would

    need to drink so that the energy used to warm it equals the energy released while

    metabolizing a 180-kcal scoop of ice cream. Indicate any assumptions you made.

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