Problem 4.3. Probability of particles moving in the same direction Consider a on
ID: 1770288 • Letter: P
Question
Problem 4.3. Probability of particles moving in the same direction Consider a one-dimensional ideal gas consisting of N5 particles each of which has the same speed , but can move in one of two directions with equal probability. The velocity of each particle is independent. What is the probability that all the particles are moving in the same direction? The example that we have just considered is an example of an isolated system. In this case the system of spins has fixed values of E, B, and N. An isolated system cannot exchange energy or matter with its surroundings nor do work on another system. The macrostate of an isolated system of particles is specified by E, V, and N (B instead of V for a magnetic system). Isolated systems are conceptually simple because all the accessible microstates have the same probability We will learn that isolated systems are described by the microcanonical ensemble (see Section 4.5).Explanation / Answer
Each particle can move in 2 -directions
there can be 5C2 ways the particles can move =10
out of this 2 ways all moving in +ve x or all in -ve x are the disired options
hence the probability of the desired event happening is
2/10 = 0.2