Explain the difference between phase space and an ensemble
Any physical system can adopt any one of a large number of microstates. The set of all these microstates is known as phase space. Statistical mechanics is concerned with calculating the probability of being in any given microstate.
The microstates that any physical system can adopt will depend on the walls that are placed around it. If the system is surrounded by walls that are impermeable to heat, work and matter then the system will be confined to a set of microstates that all have the same energy, volume and temperature. If the system has walls that can exchange heat but that are impermeable to work and matter then the system will be confined to a set of microstates that all have the same volume and temperature. However, as long as they satisfy the constraints on the volume and number of atoms microstates with all possible energies are permissible. We call the set of states that are accessible to a system surrounded by walls the ensemble. Clearly, the set of microstates in any given ensemble is a subset of the set of microstates in phase space.
<aside> 📌 SUMMARY: To make the connection between classical thermodynamics and the statistical behaviour of atoms we have to incorporate the effect of the walls surrounding the system. Walls fix the values of certain extensive variables and will thus force the system to be in one of the microstates in a subset of phase space (the ensemble).
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