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Chapter 9: 44E (page 405)
Determine the relative probability of a gas molecule being within a small range of speeds around 2vrmsto being in the same range of speeds around vrms.
The relative velocity is .
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A two-sided room contains six particles, a, b, c, d, e and f, with two on the left and four on the right.
(a) Describe the macrostate.
(b) Identify the possible microstates. (Note: With only six particles, this isn't a thermodynamic system, but the general idea still applies, and the number of combinations is tractable.)
Exercise 52 gives the Boltzmann distribution for the special case of simple harmonic oscillators, expressed in terms of the constant . Exercise 53 gives the Bose-Einstein and Fermi-Dirac distributions in that case. Consider a temperature low enough that we might expect multiple particles to crowd into lower energy states:. How many oscillators would be expected in a state of the lowest energy,? Consider all three-classically distinguishable. boson, and fermion oscillators - and comment on the differences.
Given an arbitrary thermodynamic system, which is larger. the number of possible macro-states. or the numberof possible microstates, or is it impossible to say? Explain your answer. (For most systems, both are infinite, but il is still possible to answer the question,)
Classically, what would be the average energy of a particle in a system of particles fine to move in the xy-plane while rotating about the -axis?
From equation (9-51), show that the specific heat (per mole) of a crystalline solid varies as for .
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