- #1

Dario56

- 290

- 45

Canonical ensemble is the statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature ##T##. Canonical ensemble is characterized by the three fixed variables; number of particles ##N##, volume ##V## and temperature ##T##.

What is said is that the internal energy of the system described by the canonical ensemble can change as heat can be exchanged with the reservoir. Therefore, we can calculate expectation value of internal energy by taking into account probability and energy of all possible microstates of the system.

However, if the system and reservoir are at thermal equilibrium, how can any heat be exchanged? For heat to flow, temperature difference should exist.

Also, if we for example had an one component and one phase system (like an ideal gas or a pure liquid), we know that its state is completely specified by two intensive variables (in context of the canonical ensemble; molar volume and temperature) and number of particles (number of moles). Since all these variables are specified in the canonical ensemble, internal energy and all other thermodynamic variables of the system are also specified.

If this is the case, how can internal energy change?

What is said is that the internal energy of the system described by the canonical ensemble can change as heat can be exchanged with the reservoir. Therefore, we can calculate expectation value of internal energy by taking into account probability and energy of all possible microstates of the system.

However, if the system and reservoir are at thermal equilibrium, how can any heat be exchanged? For heat to flow, temperature difference should exist.

Also, if we for example had an one component and one phase system (like an ideal gas or a pure liquid), we know that its state is completely specified by two intensive variables (in context of the canonical ensemble; molar volume and temperature) and number of particles (number of moles). Since all these variables are specified in the canonical ensemble, internal energy and all other thermodynamic variables of the system are also specified.

If this is the case, how can internal energy change?

Last edited: