Styrofoam cup Stopwatch Thermometer 10 ml sealable syringe and graph paper Dice Crushed ice Pencil Water In the Charles's law lab, use the tip of the rubber stopper in the syringe for
your volume reading: Please execute multiple trials with the cold and hot water baths. Gently push
in the stopper of the syringe and let the volume return to equilibrium. Then
record the volume in the provided table. Lab 18 Experiment 2: Probability of States
Results/Observations
Enter your data in the following tables:
If you roll two dice of different colors, the sum of the individual dice can be equal to the
numbers 2 through 12. The sum of the dice is the macrostate of this system. The numbers
on each individual die is equal to the microstate of the system. For example, if you roll a
white and black die and the white lands on a 3 and the black die lands on a 4, then the
microstate of the system is “3 and 4” while the macrostate is “7”. Given this information,
complete Table 1. A macrostate of 3 has been completed for you (dice images are
included as a visual aid).
Table 1:
Note: k is the Boltzmann constant, 1.38 x 10-23 J/K.
Prelab Question 2 - Microstate Data for 2 Dice
Possible
Number of
Microstates
Macrostate
Microstates ()
(Dice
Combinations)
2 Entropy
S = kln() 3
4
5
6
7
8
9
10
11
12
Once you know the number of possible microstates, you can determine the probability of
obtaining a certain macrostate. The probability of a macrostate, Pmacro, is equal to the
possible microstates for a given macrostate divided by the total number of possible
microstate combinations.
For example, the probability of rolling a 3, P3, is equal to 5.6%: Given this information,
complete and graph Table 2. Pmacro = number of microstates corresponding to the
macrostate, Ωmacro the total number of microstates for all possible combinations, Ωtotal
Table 2: Dice Macrostate Probability Data Macrostate Probability of Rolling a Macrostate
2 3 4 5 6 7 8 9 10 11 12 P3 = Ω3 Ωtotal 2 36 = = = 0.0555 = 5.6% 6 2 2 die 6 possible
outcomes per die (2,1) + (1,2) 2 combinations of microstates yield a macrostate of 3 Prelab Question 3 - Macrostate Probability Data
Macrostate
Probability of Rolling Macrostate
2
3
4
5
6
7
8
9
10
11
12 Insert your graph of probability vs. macrostate below. I suggest using the column
chart graph type in Excel. Instructions for this portion:
1. Take the dice and roll them on a flat surface like a table or floor. Record the macrostate
by placing a tally mark in Table 3. 2. Repeat Step 1 ninety-nine more times to get a
distribution map of the probability of macrostates for two dice. Lab 18 Experiment 2 – Dice Macrostate Probability Data – 100 Trials
Number of
Macrostate
Occurrences (Tally
Total Occurrences
Marks)
2
3
4 5
6
7
8
9
10
11
12 Lab 18 Experiment 2: Probability of States – Analysis and Discussion
Based on your experimental results, please answer the following
questions:
1. Create a graph of the number of occurrences of each macrostate. For
consistency, I suggest using the column chart graph type in Excel. Insert the
graph below. How does this graph compare to the graph you created in PreLab Question 3? 2. Given your data for one hundred rolls, calculate the probability of rolling one
specific macrostate. How does this compare to the percentages you
calculated in Pre-Lab Question 3? To answer this question, fill in the following
table.
Note: Your experimental probability percentage for each macrostate is simply
the observed tally since we executed 100 trials.
Macrostate Theoretical
Probability* Experimental
Probability Percent
Difference 2
3
4
5
6
7
8
9
10
11
12
* From the table in Prelab question 3. 3. If you repeated this experiment four times, would you expect similar results?
Why or why not? 4. How would your results be different if you rolled the dice fifty times? Five
hundred times? Optional extra credit experiment
Procedure
1.
2.
3.
4.
5. Place 24 coins face-up on a large tray.
Move the tray up and down rapidly to jostle the coins.
Carefully count and record the number that are still face-up.
Repeat steps 2-3 for a total of 15 trials.
Transfer your data into Excel and plot the results. Your plot should have
“count” for the y-axis and “trial number” on the x-axis. The plot should show
the number of heads and the number of tails for each trial, including the initial
state of 24 heads and 0 tails. Insert your plot in the lab report and answer the
questions below. Excel plot Question 1: After starting with an “ordered” set in step 1, how likely do you think it
is to arrive back in a state of “order” after shaking the tray numerous times (i.e.,
end with all heads or all tails)? Question 2: How does this experiment demonstrate the concept of entropy?

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