Our canonical ensemble was defined such that the temperature, volume, and number
ID: 791089 • Letter: O
Question
Our canonical ensemble was defined such that the temperature, volume, and number of particles were each held constant. In terms of the Legendre transform, which thermodynamic potential is fundamental in the canonical ensemble?
-The Helmholtz energy
-The internal energy
-The Gibbs energy
-The enthalpy
Which factor below does not contribute to the rotational partition function of a molecule?
-The rotational quantum number
-The nuclear and electronic spin states
-The rotational constant(s)
-The temperature of the molecule
We were able to reduce the vibrational partition function from an infinite series to a function of a single exponential, but only approximately. Which approximation below was NOT used?
-We assumed that the vibrational energy can be expressed as v?e.
-We assumed that the energy levels were close enough to allow integration instead of summation.
-We assumed that the vibrational motion is purely harmonic.
-We assumed that the separations are relatively small, due to high temperature or lower vibrational constant.
The derived partition function for an ideal gas depends on all of the physical parameters listed below except for which one?
-Molecular symmetry
-The temperature of the molecules
-The volume of the sample
-Mass of the molecules
Deriving the translational partition function is more involved than deriving the rotational and vibrational partition functions. Which statement below is NOT a reason for this?
-There are so many possible translational energy levels, that the integral does not converge to a finite value.
-The integral of translational states for a single particle must be taken over a 6-dimensional hypervolume.
-The degeneracy of translational states is not obvious because they lie so close in energy.
-Translational degrees of freedom involve interactions between all molecules in the sample, whereas rotations and vibrations do not.
The connection between the Equipartition Principle and the translational partition functions helped to demonstrate that the temperature of a system depends on the easily excited degrees of freedom. Why should this be true?
-In systems with easily excited degrees of freedom, a change in the entropy requires energy changes on the order of thermal energy.
-In systems with easily excited degrees of freedom, small increases in the pressure make excited states more accessible,
increasing the temperature.
-In systems with easily excited degrees of freedom, the potential energy is no longer dependent on the temperature of the system.
-In systems with easily excited degrees of freedom, thermal energy is sufficient to allow one to treat the energy levels as a continuum.
The connection between the Maxwell-Boltzmann distribution and the translational partition function allowed us to better understand the distribution of speeds. Which statement below is NOT a consequence of the translational partition function?
-The population of the lowest speeds is very small.
-The pressure of the gas increases as the velocity increases.
-An increase in the temperature will result in shifting the distribution to higher energies.
-The population of the highest speeds is very small.
Explanation / Answer
a.-The Helmholtz energy
b.The nuclear and electronic spin states
c.We assumed that the separations are relatively small,
due to high temperature or lower vibrational constant.
d.The volume of the sample.
e. The integral of translational states for a single particle must be taken over a 6-dimensional hypervolume.
f.In systems with easily excited degrees of freedom, the
potential energy is no longer dependent on the temperature of the system.
g.The population of the highest speeds is very small.
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