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Chapter 9: Q5CQ (page 402)

Defend or refuel the following claim: An energy distribution, such as the Boltzmann distribution. specifies the microstate of a thermodynamic system.

Short Answer

Expert verified

The statement above is not completely accurate. In principle, energy distributions such as the Boltzmann distribution determines the likelihood of several particles in a thermodynamic system to occupy a specific microstate. Simply put, energy distributions do not give an individual-particle energy, but a range of possible energies that can be occupied for a given temperature

Step by step solution

01

Boltzmann distribution

A Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system.

02

reason for the enormous number of possible microstates

The reason for this is the enormous number of possible microstates to be inhabited resulting in the chaotic behaviour of the individual motion of the molecules. As a result, probability distributions are formulated to describe a statistical ensemble of microstates to describe the macroscopic properties of the system such as temperature and internal energy.

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Most popular questions from this chapter

Exercise 54 calculates the three oscillator distributions'E=0values in the special case wherekBTis15ξ. Using a very common approximation technique. show that in the more general low-temperature limit,kBT≪ε,theoccupation numbers becomeδ/kBT,e5/kBT, and 1, for the distinguishable. boson. and fermion cases, respectively. Comment on these results. (Note: Although we assume thatkBT≪Nω0/(2s+1). we also still assume that levels are closely spaced-that is kB↑≫hω0.),

Four distinguishable Hamonic oscillators a,b,c,andd may exchange energy. The energies allowed particleareEa=naℏω0: those allowed particlebareEb=nbℏω0, and so on. Consider an overall state (macro-state) in which the total energy is3ℏω0. One possible microstate would have particles a,b,andcin theirn=0states and particle d in itsn=3states that is,na,nb,ncnd=(0,0,0,3).

(a) List all possible microstates, (b) What is the probability that a given particle will be in itsn=0 state? (c) Answer part (b) for all other possible values of n. (d) Plot the probability versus n.

A "cold" subject,T1=300K, is briefly put in contact with s "hut" object,T2=400K, and60Jof heat flows frum the hot object io the cold use. The objects are then spiralled. their temperatures having changed negligibly due ko their large sizes. (a) What are the changes in entropy of each object and the system as a whole?

(b) Knowing only this these objects are in contact and at the given temperatures, what is the ratio of the probabilities of their being found in the second (final) state for that of their being found in the first (initial) state? What dies chis result suggest?

The Fermi energy in a quantum gas depends inversely on the volume, Basing your answer on Simple Chapter 5 type quantum mechanics (not such quaint notions as squeezing classical particles of finite volume into a container too small). Explain why.

The maximum wavelength light that will eject electrons from metal I via the photoelectric effect is410nm. For metal2, it is280nm. What would be the potential difference if these two metals were put in contact?
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