4.02 Absolute Zero


Purpose: To explore the concept of absolute zero

Introduction: In principle, there is no upper limit to temperature. As thermal motion increases, a solid object first melts and then vaporizes. As the temperature is further increased, molecules break up into atoms, and atoms lose some or all of their electrons, forming a plasma. Plasmas exist in stars where the temperature is many millions of degrees Celsius.

However, there is a definite lower limit to temperature. Experiments in the nineteenth century showed that there is a limit to coldness. At this lowest temperature, no more energy can be extracted from a substance. What is the lowest possible temperature? The name absolute zero has been given to the lowest possible theoretical temperature. In this activity, you will use Graphical Analysis to experience the prediction method that has led to absolute zero.

Materials: Graphical Analysis

Procedure:

  1. Carefully read and study the tutorial below.

  2. Complete the activity and answer the associated questions.


Tutorial:
  1. Pressure and Absolute Zero: The value of absolute zero was found in the 1800s by experimenters who discovered that all gases contract by the same proportion when temperature is decreased. It was found that any gas at zero degrees Celsius, regardless of its initial pressure or volume, changes by 1/273 of its initial volume for each one degree Celsius change in temperature, when pressure is held constant. For example, when the temperature is reduced to -100 degrees Celsius, the volume of the gas is reduced by 100/273. More striking, if a gas at zero degrees Celsius were cooled to -273 degrees Celsius, its volume would be reduced by 273/273 and become zero. Clearly, we cannot have a substance with zero volume.
  1. Temperature and Absolute Zero: It was also found that the pressure of any gas in a chamber of fixed volume would change by 1/273 for each one degree Celsius change. So gas in a container of fixed volume cooled to -273 Celsius would have no pressure whatsoever. In reality, every gas becomes a liquid before it gets this cold.
  1. Kinetic Energy and Absolute Zero: These decreases in volume and pressure by increments of 1/273 suggested the idea of the lowest possible temperature (-273 Celsius). This temperature is called absolute zero. Keep in mind, however, that at absolute zero atoms have a small amount of kinetic energy called zero-point energy.
  1. Definition of Absolute Zero: In his book Conceptual Physics, Paul Hewitt defines absolute zero as "the temperature at which a substance has no kinetic energy per particle (thermal) to give up." This temperature corresponds to zero Kelvin. [Source: © 1997 Paul Hewitt]

  1. The Gas Law of Gay-Lussac (Joseph Gay-Lussac - 1778-1850): Although gases do not have a definite shape or a definite volume, except for that defined by their containers, a relationship between temperature and volume can be developed for enclosed gases.

    The product of the pressure and the volume of an ideal gas is directly proportional to the product of the number of molecules in the gas and its absolute temperature. This proportionality expressed mathematically as

    PV alpha nT

    P is the pressure
    V is the volume
    alpha denotes a relationship
    n is the number of molecules
    T is the absolute temperature (Kelvin)

    Today's activity uses Gay-Lussac's Law, which states the following: "When the volume of the enclosed gas and the number of molecules of the enclosed gas remain the same, the absolute temperature is directly related to the pressure exerted by the enclosed gas." As the absolute temperature increased, the average kinetic energy of the molecules increases. The molecules collide with the container walls with a greater force and more frequently.

    This relationship is

    P alpha T
    P is the pressure
    alpha denotes a relationship
    T is the absolute temperature of the gas (Kelvin)

    The graph below represents Gay-Lussac's Law:
graph showing pressure versus absolute  temperature
Analyzing the graph:
A fixed mass of gas in an enclosed rigid container with an initial pressure of 5.0 Pascals and absolute temperature of 200. K is heated such that the gas reaches an absolute temperature of 400. K. What will the pressure be when the gas reaches the absolute temperature of 400. K (Notice the absolute temperature doubled)?

The equation for a straight line:

y = m x
P = k T

Solving equation for constant of proportionality k:

k = P/T

Setting the constant equal to each other gives you the equation for Gay-Lussac's Law:

k = k

P1 = k T1 k = P1/T1 Therefore:

P2 = k T2

k = P2/T2

P1/T1= P2/T2


Using the graph or the equation, answer the following question:
A fixed mass of gas at initial pressure of 5.0 Pascals and absolute temperature of 200. K will be at what absolute temperature when the pressure is 8.0 Pascals?
P1 = 5.0 Pascals
T1 = 200. K
P2 = 8.0 Pascals
T2 = ?

P1/T1 = P2/T2
T2 = (P2T1)/P1
T2 = [(8.0 Pascals)( 200. K)]/5.0 Pascals
T2 = 320 K
If you look at the graph you will see that the absolute temperature reading for 8.0 Pascals of pressure is approximately 320 K.

Activity:
  1. Here is a simple diagram of an absolute zero demonstrator. This simple apparatus can be used to predict the value of absolute zero. This apparatus is sometimes referred to as a constant volume thermometer because the volume of the metal sphere stays essentially constant while the pressure reading changes with a change in temperature.
absolute zero demonstrator graphic

Sample data is shown in Table 1 shown below.


Table 1

Trials Temperature
(degrees Celsius)
Pressure
(psi)
1 100. 18.5
2 23.0 14.7
3 0 13.5

  1. Use Graphical Analysis to make a graph of the data from Table 1. Be sure to use the headings of the columns on Table 1 as the labels for the x-axis and y-axis of the graph.
  1. Double click in the center of your graph to bring up the "Graph Options" dialogue box.

graph options window

Select Select the Axes Options tab.
Change the X-axis scaling from Autoscale to Manual using the toggle arrow and set the
left limit to -300 and the right to 100

 

  1. Use the same procedure described in step 3 to make changes to the y axis. Change the limits of the y axis to these: top limit is 20 and the bottom limit is 0.
  1. Save your graph. Remember to begin the graph filename with your initials.

Questions:

  1. Visit the following URL: What is absolute zero?

    1. According to this website, what is the definition of "absolute zero"?

    2. Why is the Kelvin scale especially helpful when studying absolute zero?

    3. What is the value of absolute zero on the Kelvin scale? the Celsius scale, and the Fahrenheit scale?

  2. Visit the following URL: Physlink.com Absolute Zero or Ask a Scientist: Absolute Zero

    1. According to this website, what type of experiments led to the idea of absolute zero?

    2. Describe scientists' attempts to reach absolute zero.

  3. Visit the following URL: New State of Matter Seen Near Absolute Zero . What is a Bose-Einstein condensate?

  1. According to the information you have obtained, you know that absolute zero is about -273 degrees Celsius. You will now use your graph to predict this value based on the laboratory data presented in this activity.

    1. Think back to the Galileo Gardens activity "Prediction Tips." You will be using the same prediction techniques to find the value of absolute zero. Go back to your graph from step 5 above. Be sure that the graph window is active. From the menu bar at the top of the screen, select "Analyze." Choose "Automatic Curve Fit." Select the proper function based on the arrangement of the data points.

    2. Now select "Interpolate" from the Analysis menu. You can view this in the graphic at right. Move your cursor along the line of the graph until the y axis value is zero (0). The corresponding x value is the predicted value of absolute zero. What is the predicted value of absolute zero shown on your graph?

 

analyze menu

4.02 Discussion Question:

Go to the discussion area and post an answer to this question. Respond to at least one other person and explain why you agree or disagree with his/her comment.

  1. Now that you have studied the concept of absolute zero, do you think this temperature will ever be reached? Explain your answer.


Joule's Jungle

4.02 Scorcher-Absolute Zero

  1. Submit your completed work.

  2. Be sure to save your work as an .rtf file. Include both the questions and the appropriate answers.


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