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Chapter 9: Q3CQ (page 402)

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,)

Short Answer

Expert verified

None can be measured; we know that there are more possible microstates

Step by step solution

01

microstates

Microstate is a term that describes the microscopic properties of a thermodynamic system.

02

possible number of microstates

Greater number is of the possible microstates, this is only theoretical simply because no one can keep track of each molecule and its position.

Knowing the number of molecules on each side would be knowing the macro-state of the system, but knowing each molecule where it is, specifying the actual molecule, is giving more options - microstates.

Although none can be measured, we know that there are more possible microstates.

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Most popular questions from this chapter

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

When a star has nearly bumped up its intimal fuel, it may become a white dwarf. It is crushed under its own enormous gravitational forces to the point at which the exclusion principle for the electrons becomes a factor. A smaller size would decrease the gravitational potential energy, but assuming the electrons to be packed into the lowest energy states consistent with the exclusion principle, "squeezing" the potential well necessarily increases the energies of all the electrons (by shortening their wavelengths). If gravitation and the electron exclusion principle are the only factors, there is minimum total energy and corresponding equilibrium radius.

(a) Treat the electrons in a white dwarf as a quantum gas. The minimum energy allowed by the exclusion principle (see Exercise 67) is
Uclocimns=310(3蟺2h3me32V)23N53

Note that as the volume Vis decreased, the energy does increase. For a neutral star. the number of electrons, N, equals the number of protons. If protons account for half of the white dwarf's mass M (neutrons accounting for the other half). Show that the minimum electron energy may be written

Uelectrons=9h280me(3蟺2M5mp5)131R2

Where, R is the star's radius?

(b) The gravitational potential energy of a sphere of mass Mand radius Ris given by

Ugray=-35GM2R

Taking both factors into account, show that the minimum total energy occurs when

R=3h28G(3蟺2me3mp5M)13

(c) Evaluate this radius for a star whose mass is equal to that of our Sun 2x1030kg.

(d) White dwarfs are comparable to the size of Earth. Does the value in part (c) agree?

There are more permutations of particle labels when two particles have energy0 and two have energy1 than when three particles have energy 0and one has energy . 2(The total energiesarethe same.) From this observation alone argue that the Boltzmann distribution should be lower than the Bose-Einstein at the lower energy level.

In Exercise 35, a simple two-state system is studied. Assume that the particles are distinguishable. Determine the molar specific heat Cvof this material and plot it versus T. Explain qualitatively why it should behave as it does.

Using the result of part (a) in Exercise 74 , determine the number of photons per unit volume in outer space. whose temperature - the so-called cosmic background temperature-is2.7K .
See all solutions

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