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Chapter 9: Q6CQ (page 402)

Not surprisingly. in a collection of oscillators, as in other thermodynamic systems, raising the temperature causes particles' energies to increase. Why shouldn’t point be reached where there are more panicles in some high energy state than in a lower energy. state? (The fundamental idea, not a formula that might arise from it. is the object.)

Short Answer

Expert verified

Whereby increasing the temperature causes an increase in the particles' energies, doing so warrants a drastic change in the number of ways a particular energy state can be occupied. As a result, particles occupying the least energy state will still tend to have the most freedom to re-allocate the energy in response to an increase in temperature.

Step by step solution

01

thermodynamic system

The field of science known as thermodynamics studies temperature, heat, and the interactions between heat and other types of energy.

02

Step 2:higher energy states are more probable than lower energy states.

Therefore still, the most likely energy state that can be occupied by particle is of that corresponding to the lowest energy state. For this reason, it not plausible for the energy to be re-distributed in way that higher energy states are more probable than lower energy states.

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Most popular questions from this chapter

Exercise 52 gives the Boltzmann distribution for the special case of simple harmonic oscillators, expressed in terms of the constantε, ≡Nℏω0/(2s+1)and Exercise 53 gives the two quantum distributions in that case. Show that both quantum distributions converge to the Boltzmann in the limitkBT≫.

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.

By considering its constituents, determine the dimensions (e.g. length, distance over lime. etc.) of the denominator in equation(9−26). Why is the result sensible?

Consider a system of two identical objects heading straight toward each other. What would qualify and whit would disqualify the system as a thermodynamic systemin, and how, if at all, would this relate to the elasticity of the collision?

The exact probabilities of equation (9-9) rest on the claim that the number of ways of addingNdistinct non-negative integer to give a total ofM is (M+N-1)![M!(N-1)!] . One way to prove it involves the following trick. It represents two ways that Ndistinct integers can add toM-9 and5, respectively. In this special case.

The X's represent the total of the integers, M-each row has 5. The 1'srepresent "dividers" between the distinct integers of which there will of course be N-Ieach row has8 . The first row says thatn1 is3 (three X'sbefore the divider between it andn2 ), n2is0 (noX's between its left divider withn1 and its right divider withn3 ),n3 ) is1 . n4throughn6 are0 , n7is1 , and n8and n9are0 . The second row says that n2is 2. n6is 1, n9is2 , and all othern are0 . Further rows could account for all possible ways that the integers can add toM . Argue that properly applied, the binomial coefficient (discussed in AppendixJ ) can be invoked to give the correct total number of ways for anyN andM .
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