For which system below would quantum effects be least noticeable? -The collision
ID: 790779 • Letter: F
Question
For which system below would quantum effects be least noticeable?
-The collision of two N2 molecules in a gas, which changes the rotational energy of both
-Polarization of the electron density of ethanol resulting in excitation of vibrational motions
-An electron-sized particle moving in a 1 m3 box as the temperature decreases by 10 degrees
-A hydrogen atom being struck by a UV photon
We have dealt with two different ensembles, canonical and microcanonical. Which of the following statements is inaccurate regarding these ensembles?
-The canonical ensemble is always considered as a subset of a larger reservoir, which acts as the surroundings.
-The microcanonical ensemble is defined to have constant energy, volume, and composition.
-The microcanonical ensemble is a smaller subset of microstates of the canonical ensemble.
-The canonical ensemble is generally more useful than the microcanonical for chemical processes.
Which statement below is most correct regarding the partition function of an ensemble?
-For a given temperature, the high-energy contributions to the partition function are more heavily weighted.
-Once a partition function is defined in a specific ensemble, it is valid in all other ensembles.
-It tells us the numerical order of the energy levels for a given system.
-It provides a measure of the energy levels available to a system at a given temperature.
Consider a cup-carrier from your favorite take-out restaurant. The carrier can hold four cups, and you have to place two cups (one large, one small) into the carrier, with no preference for position. How many microstates can you form with two cups in the four spaces?
-12
-8
-16
-6
Boltzmann's definition of the entropy was a breakthrough in understanding statistical thermodynamics. What is the best definition of Boltzmann's entropy?
-The Boltzmann entropy is a count of the total distinct microstates in a system.
-The Boltzmann entropy is a measure of the randomness of an ensemble.
-The Boltzmann entropy is a count of the accessible energy levels at a given temperature.
-The Boltzmann entropy is a measure of the useful work available in an ensemble.
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
The equipartition principle can be used to estimate the constant volume heat capacities of gases. Under which circumstances would the full equipartition heat capacity most closely approximate the measured value of CV?
-A sample of N2 gas at 373K
-A sample of propane gas (C3H8) at room temperature
-A sample of water vapor at 373K
-A sample of Br2 vapor at room temperature
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.
When dealing with quantum energy levels, there are several important factors to consider. Which concept below is NOT important to quantum energy levels?
-The set of quantum numbers
-Degeneracy
-The deBroglie wavelength
-The ground state
Explanation / Answer
entholpy is constant
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