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Chapter 12: Q11Q (page 507)

Explain qualitatively the basis for the Boltzmann distribution. Never mind the details of the math for the moment. Focus on the trade-offs involved with giving energy to a single oscillator vs. giving that energy to a large object.

Short Answer

Expert verified

The loss of energy of a system represents that it saturates to a certain state and when the energy level is more the system fluctuates heavily and cools down to one desirable state.

Step by step solution

01

Understanding the Boltzmann distribution

In this problem, Boltzmann distribution is a probability function used in statistical physics to characterize state of a system of particles, with respect to temperature and energy.

02

Qualitative explanation about Boltzmann distribution

The system can exist in several states; however, the chance of being in certain subset of states is higher than other.

The chance itself is parameterized over certain property values. As a system loses energy, it saturates to a certain state, when the energy is high, it fluctuates heavily and as it cools down it stabilizes to one of desirable states.

The Maxwell-Boltzmann distribution is given below.

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Most popular questions from this chapter

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Object A and object B are two identical microscopic objects. Figure 12.55 below shows the number of ways to arrange energy in one of these objects, as a function of the amount of energy in the object.


(Figure 12.55)

(a)When there are\({\bf{1}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 20}}}}{\bf{J}}\)of energy in object A, what is the entropy of this object? (b) When there are\({\bf{1}}{\bf{.4 \times 1}}{{\bf{0}}^{{\bf{ - 20}}}}{\bf{J}}\)of energy in object B, what is the entropy of this object? (c) Now the two objects are placed in contact with each other. At this moment, before there is time for any energy flow between the objects, what is the entropy of the combined system of objects A and B?

What is the advantage of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms (natural logarithm of the number of microstates)?
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