Search results
Results from the WOW.Com Content Network
The partition function is a function of the temperature T and the microstate energies E 1, E 2, E 3, etc. The microstate energies are determined by other thermodynamic variables, such as the number of particles and the volume, as well as microscopic quantities like the mass of the constituent particles.
These three equations, along with the free energy in terms of the partition function, = , allow an efficient way of calculating thermodynamic variables of interest given the partition function and are often used in density of state calculations. One can also do Legendre transformations for different systems. For example, for a system with a ...
For quasi-static and reversible processes, the first law of thermodynamics is: d U = δ Q − δ W {\displaystyle dU=\delta Q-\delta W} where δQ is the heat supplied to the system and δW is the work done by the system.
Rotational energies are quantized. For a diatomic molecule like CO or HCl, or a linear polyatomic molecule like OCS in its ground vibrational state, the allowed rotational energies in the rigid rotor approximation are = = (+) = (+). J is the quantum number for total rotational angular momentum and takes all integer values starting at zero, i.e., =,,, …, = is the rotational constant, and is ...
The generalized version of the partition function provides the complete framework for working with ensemble averages in thermodynamics, information theory, statistical mechanics and quantum mechanics. The microcanonical ensemble represents an isolated system in which energy (E), volume (V) and the number of particles (N) are all constant.
In statistical mechanics, the translational partition function, is that part of the partition function resulting from the movement (translation) of the center of mass. For a single atom or molecule in a low pressure gas, neglecting the interactions of molecules , the canonical ensemble q T {\displaystyle q_{T}} can be approximated by: [ 1 ]
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.
What has been presented above is essentially a derivation of the canonical partition function. As one can see by comparing the definitions, the Boltzmann sum over states is equal to the canonical partition function. Exactly the same approach can be used to derive Fermi–Dirac and Bose–Einstein statistics.