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Briefly explain how the thermodynamic properties of a macroscopic assembly of molecules can be determined from the molecular partition function.
Accepted Answer
The molecular partition function, denoted by 'Q', encapsulates all the possible energy states a molecule can occupy at a given temperature. This information is crucial for understanding the macroscopic thermodynamic properties of a system. Here's how:
Internal Energy (U): The average energy of a system is directly related to the partition function by the equation: U = - (∂ ln Q / ∂ β), where β = 1/kT (k is Boltzmann's constant, T is temperature).
Entropy (S): Entropy, a measure of disorder, is related to the partition function by: S = k (ln Q + βU).
Helmholtz Free Energy (A): This thermodynamic potential relates internal energy, entropy, and temperature: A = -kT ln Q.
Therefore, by calculating the molecular partition function, one can derive fundamental thermodynamic properties like internal energy, entropy, and free energy for a macroscopic assembly of molecules.
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