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Consider a classical system of N very weakly interacting diatomic molecules, in a container of volume V , at a given tem- perature T . The Hamiltonian of a single molecule is given by
where k > 0 is an elastic constant. Obtain an expression for the Helmholtz free energy of this system. Calculate the specific heat at constant volume. Calculate the mean molecular diameter,
Now consider another Hamiltonian, of the form ε
where ε and ro are positive constants, and
What are the changes in your previous answers?
Physics
Taking into account the thermodynamic limit (V → ∞ ), the first Hamiltonian is associated with the partition function
from which we obtain the Helmholtz free energy (and the value of D). It interesting to check the constant value of the molecular specific heat, s = (9/2) kB.
The second Hamiltonian represents a more complicated model of a diatomic molecule. The partition function is given by
where
Now it is interesting to obtain the specific heat as a function of temperature.
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