consider a system that consists of two six sided dice. a. how many total unique
ID: 1553981 • Letter: C
Question
consider a system that consists of two six sided dice.
a. how many total unique outcomes are there?
b. create a table and list all the possible microstates, their corresponding multiplicities and probabilities. what is the most and least accessible macrostate? Does the sum of all the multiplicities equal the value calculated and part A?
c. get to pair of dice and roll them yourself until you roll one of each possible macrostate be sure to keep track of the results of which role. how many rolls did it take to obtain each microstate at least once what is your most and least probable macrostates? where are the percentages of all rolls on par with what you calculated in Part B?
Explanation / Answer
a) The total possible outcome on throw of two dice would be 36
6x6
(b)
smple space woul be;
[(1,1);(1,2). . . . . . . . . . .(1,6)
.......................................
(4,1)..................................
............................................(6,6)]
b) the possibility of each macrostate would be 1/36
In this dice example, there were 2 constituents and each constituent had 6 possible states, leading to 6 × 6 = 62 = 36 possible microstates.
(c)We call each such Z value a macrostate. Notice that for each microstate there is a unique macrostate. But there can be many microstates corresponding to a macrostate. If all the microstates are equally probable, we can estimate the probability of the macrostate by counting the number of microstates corresponding to a macrostate. We call the number of microstates in a given macrostate the multiplicity of the macrostate. Look at multiplicity of two-dice system. For the two dice system we need to count the number of ways we can make a macrostate. We call this the multiplicity of the macrostate. And we need to divide by the total number of microstates to find the probability. For example, we can divide the microstates into a set of macrostates corresponding to the sum of the two dice. The possible macrostates are then 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 What are the probabilities of the various states? We can see this by looking at a matrix representing all possible microstates
yes, sum of all the multiplicities equal the value calculated and part A
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