NVT ensemble thermodynamics

With the partition function at hand, we can derive expressions for all important thermodynamic properties. 

The energy of a system with constant NVT fluctuates. The ensemble average is the macroscopically observable internal energy, U, with 

The introduction of the constant Icb in E q. 5.27 and consequently in Eq. 5.26 is needed to properly account for property units. This constant is Boltzmann s constant. 

The canonical variables of the Helmholtz free energy for closed systems are the temperature T and volume E, as is apparent in Eq. 5.22. A canonical ensemble system is at equilibrium then when the number of available microscopic states is maximum, that is when the partition function is maximum, or equivalently when its Helmholtz free energy is minimum. 

With the canonical partition function Q(N, V, T) we can also calculate other thermodynamic properties, such as the pressure. 

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