Question

What is phase space? And also what is relaxation time? ( Thermodynamics)

Answer 1

a) The phase space is a method used to represent all the possible configurations of a system.

In any co- ordinate system, in 3 dimensions, the position of any particle is represented by three values that are the distances or angles. While this can represent the position of a particle anywhere in the universe, this does not describe the system as a whole. For a complete description of the system, the motion of the particle is also to be quantified.

In physics, this is done by defining the position as well as momentum of the particle. If there is a single particle in one dimension, to completely describe the particle, there must be a value of position and a value of momentum of the particle.

If there are N particles, there must be 2N points to describe the particle as a whole in 1 dimension.

If the system is in 3D, there must be 6N co ordinates to represent the system completely.

This representation has to be done in a space, just like the real space. The space in which the particle is described is called phase space.

In exact words, the phase space is a collection of all the possible states of a system, just like the set {1,2,3,4,5,6} is the collection of all the possible states of a dice. It is a type of co-ordinate system.

b) The term relaxation time is used in a wide variety of contexts in physics.

In the most general terms, it is the time taken for a system to come back into its initial condition, after a change has occured.

In terms of atomic interactions, it is the time taken by the atom to come back into its ground state (stable state) once it is excited to an unstable excited state due to some reason, like collision with a photon (light), collision with another atom, or a charged particle.

In terms of kinetic theory, it is the time between two collisions. The atoms in a gas ( or electrons in a conductor) is in a non stop random motion. During this motion, they tend to collide with other atoms in a regular interval. (given that there is a large no of particles) The average time difference between any two collisions is called relaxation time.