Calculating Absolute Zero with Charles’s Law

According to the Kinetic Theory atoms of a gas are so small that they can be considered to have no volume compared to their surrounding empty space. It is also stated that the velocity of the particles is directly proportional to the temperature of the gas.

It can be inferred from these theories that the particles motion can be stopped completely by bringing the gas to an extremely low temperature. The temperature at which all motion stops is called ABSOLUTE ZERO.

Theoretically there can be no temperature below this value, so this is used as the absolute scale. The scales we are used to using (Celsius and Fahrenheit) were based on the freezing point of water. This is very high relative to Absolute Zero.

Charles’ Law states that there is direct relationship between Temperature and Volume of a Gas if the pressure is held constant. The Law is states as follows: volume  Cons tan t temperature or V  Cons tant T

This Law can be used to experimentally find the value of absolute zero. You will use a graphing method to find the equivalent value of absolute zero in the Celsius temperature scale.

Experimental Method

A gas is placed in a cylinder under a movable piston. A weight is placed on the piston creating a constant force on the piston. The temperature of the gas is varied and the corresponding volumes are recorded. The data below is from the experiment.

Piston Weight of Temperature Volume RATIO Known (Celsius) (liters) V/T Value 273 .1094 100 .0748 10 .0568 1 .0545 0 .0544 -73 .0403

Gas Molecules in motion

Calculation of Absolute Zero 1. Calculate the ratio (V/T) to verify that the gas obeys Charles Law. 2. Use an Excel Spread sheet to plot the data from the experiment. a. Input the independent variable in the A column b. Input the dependent variable in the B column 3. Creating the graph a. Select the data by clicking and dragging over the data b. Click on the Chart Wizard c. On the X-axis of the graph use a scale that starts at –300 degrees C and goes up to 300 d. On the Y-axis of the graph use a scale that starts at zero an goes to .11 e. Use and X-Y Scatter Plot and only the data points f. Include your name in the title as follows “Name” Absolute Zero Calculation g. Y-axis title “Volume (ml)” h. X-axis title “Temperature (C)” 4. Calculating Absolute Zero a. When you have made the graph with the proper titles, and scales print it out b. With a ruler draw the line of best fit through the points and project it until it crosses the x-axis c. The point at which it crosses the x-axis is the value of Absolute Zero

Questions:

1. Show the gas follows Charles Law? How do you know?

To show the gas follows Charles’s Law, the ratio of V/T should be calculated. If the gas follows the law, the ratio V/T should be the same (theoretically) in every case.

NOTE: It should be noted that the Temperatures must be in the absolute scale to show the gas follows Charles’s Law.

Ratio (V/T) Calculated using Temperatures in Celsius

V/T Temperature Volume (Ratio) (Celsius) (liters) If the ratio is calculated using temperature 273 0.1094 0.00040 values in the Celsius Scale there are values 100 0.0748 0.00075 that do not make sense. These are negative 10 0.0568 0.00568 and UNDEFINED. The undefined value 1 0.0545 0.05450 occurs because there is division by zero. 0 0.0544 UNDEFINED -73 0.0403 -0.00055

Ratio (V/T) Calculated using Temperatures in Kelvin

Temperature Volume V/T (Kelvin) (liters) (Ratio) = C +273 If the ratio is calculated using temperature 546 0.1094 0.00020 values in the Kelvin Scale shows the ratio 373 0.0748 0.00020 to be consistent throughout the values 283 0.0568 0.00020 given. All values are 0.00020. 274 0.0545 0.00020 273 0.0544 0.00020 200 0.0403 0.00020

2. What is your value for Absolute Zero in the Celsius Scale?

From the graph you have created you should be able to tell that the graph crosses the x-axis at approximately –270 degrees Celsius.

Calculation of Absolute Zero with Charles Law

0.12

0.1

0.08

0.06

0.04 Volume (liters)

0.02

0 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 Temperature (C)

3. Calculate the slope of the line (rise/run)?

 RISE y2 y1 .1094 .0403 .0691 SLOPE = = = = = .0001997 RUN  273  (73) 346 x2 x1

Calculation of Absolute Zero with Charles Law

0.12

0.1

0.08

0.06

0.04 Volume (liters) Volume

0.02

0 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 Temperature (C)

4. Using the slope and one of the data points and some Algebra calculate the value of Absolute Zero? How does it compare to the value you found graphically?

SLOPE = .0001997

Linear Equation: Y = mX + b m - slope Y – represents the Volume (dependent variable, V ) X – represents the Temperature (independent variable, T ) b – the y intercept, given as (0, .0544)

Y = mX + b

V = (.0001997 × T) + .0544

We want to know the value of Temperature (T) when the Volume is zero, so we plug in zero for the Volume (V) and solve for the Temperature (T). This is where your graph crosses the X-axis.

0 = (.0001997 × T) + .0544

subtract .0544 from both sides

{0 - .0544} = {(.0001997 × T) + .0544 - .0544}

this gives

-.0544 = .0001997 × T

divide both sides by .0001997

-.0544 = .0001997 × T .0001997 .0001997

divide to get

-272.4 = T (Absolute zero C)