Consider a container with two different parts, A and B. We will assume for the e

Question

Consider a container with two different parts, A and B. We will assume for the experiments below that we have an easy way to see whether molecules are in part A or part B of the box. (a) If we put a single molecule of an ideal gas into the container and the dividing line for the box is arranged such that VA = VB, what is the probability, WA, that the molecule will be found on the A side of the box when we look at it? (b) Suppose that we rearrange the dividing line in the box so that part A now takes 3/4 of the box while part B takes 1/4 of the box. What is the probability, WA, that the molecule will be in part A? What is the probability, WH, that it will be in part B? (C) Write a general expression for the probability, WA, that the molecule will be found in the A side of the box.

Explanation / Answer

a) the probability of finding a molecule in either of compartment will be 1/2 = 0.5
b) The probaility of finding the molecule in part A = 3/4 while that in B will be 1/4

c) The probability will be = area of A / total number of parts of A and B

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