An analogy: a child with blocks and constraints on physical systems. A certain child’s room is

partitioned into 100 squares. His toy box in the corner is exactly one square in size and contains

some number of blocks. When he plays with the toys, he tends to throw them around and evenly

scatter them about the room.

a) Assume that there are now three blocks (red, green, and blue). Also assume that all three blocks

can fit on one square. How many accessible microstates are there for this system, if they are all

in the toy box, lid is closed, and the lid is locked in the closed position? (All the other constraints

imposed in the story still apply.)

b) What is the total number of accessible microstates for this system, if the toy-box lid is opened?

c) If the boy plays for a long time with all the blocks (and randomly leaves them in the toy box or on

one of the floor squares), what is the probability of finding the red block in the toy box, the blue

box on square #15, and the green block on square #75? Explain how you determined this result.

d) Again, after a long time, what is the probability of finding the red block in the toy box independently

of where the blue and green blocks are?

e) How would probability in (d) change if we asked for it after the boy had been playing for only 15

seconds? Explain why.

f) Explain what condition must be satisfied to say that a system is equally likely to be in any of its

accessible microstates

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Answer :-(i)Given that the clata,タ.A child with blocks and constraints on pheyical systemAlertain child's room is partioned into 100 squares.Ners toy box in the corner is Exactly one square insye and Contains some number of backs. When he phys with the toys, he tends to throw them around and Everly Scatter them about the room.(a) Since toy box is fixed at one bocation in the corner and it is closed so there is only, one acusible state for this system.(b) Given that the data,The total number of aussible microstates for this System, if the system. if the toy box lid is Opened.If toy box lid is open thin Zach blok can be in any of the 100 Squares (99 squar plas toybor) also any one Square can aucomodate all 3 So total no. of auessible microtates for this system is100 \times 100 \times 100=1000000 .(2)(c) Red bbuk in the toy box is one only one Stale as toy box is fixed in corner. Also, Green box in squars # 75 and blue box in Square # 15. Combined, this only one possible microtable as all 3 paritions are fixed.So probalility =\frac{1}{1000000}.(d) Reb black in tay box is one possibility but Hue block in any square is 100 possibility & similarly for green block so total no-of acussible microtabe is 1 \times 100 \times 100^{\circ}\text { Probability }=\frac{10000}{1000000}=\frac{1}{100}(e) Suppose initally all bockes are in box and the boy came and start playing with them. Suppose system has not reached.(*) The condition must be satisfied to say that a System is equally likely to be in any of its accissible microstates.Thank You T ...