This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Boltzmann Distribution”.
1. At low temperature, low – lying states close to the ground energy levels are overly populated.
a) True
b) False
View Answer
Explanation: At higher temperatures, the molecules are spread over different states in several energy levels but the same trend is not observed at lower temperatures. At temperatures below 5K, molecules are near or at the ground state thus making it overly populated.
2. What does Boltzmann distribution tell us?
a) Energy levels
b) Distribution of molecules at different energy levels
c) Distribution of electrons in a molecule
d) Magnitude of different energy levels of a molecule
View Answer
Explanation: The Boltzmann distribution is a probability distribution of how molecules are at different energy levels. It is given by:
N\(_j^*\) = N\(\frac {g_j e^{- \frac {ε_j^{‘}}{kT}}}{∑_jg_j e^{ – \frac {ε_j^{‘}}{kT}}} \)
Where, ε\(_j^{‘}\) is total energy
gj are the degenerate states
N are the number of molecules
3. What is a partition function Q a function of?
a) Volume
b) Temperature
c) Temperature and volume
d) Volume and mass
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Explanation: The partition function Q is also known as the state sum. It is defined by the formula:
Q = ∑jgje\(^{- \frac {ε_j^{‘}}{kT}}\)
This partition function has its use in statistical thermodynamics and is a function of both temperature and volume.
4. Boltzmann distribution tells us the distribution of molecules in an unsteady system.
a) True
b) False
View Answer
Explanation: Boltzmann distribution helps in analyzing the energy state εj in which the molecule or atom lies within a system of N – molecules. This distribution is provided for a system of molecules/atoms which is in thermodynamic equilibrium.
5. How does the probability of finding molecule in an energy state vary?
a) Parabolic
b) Exponential
c) Hyperbolic
d) Linear
View Answer
Explanation: On observing the equation of finding the molecule in a particular energy state as given by Boltzmann distribution law, we see that the graph varies exponentially as energy εj divided by kT (where k is the Boltzmann constant).
Sanfoundry Global Education & Learning Series – Aerodynamics.
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