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Chapter 2: Q. 2.7 (page 57)

For an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove equation 2.9.

Short Answer

Expert verified

Possible microstates of dots and vertical lines are 惟(4,2)=10

Step by step solution

01

 Step :1 Possible microstates

For four oscillators N=4and two unit of energyq=2 , the possible microstates are:

02

 Step :2 Using the general formula

Using the general formula for the multiplicity of Einstein solid with N=4and q=2:

localid="1650337110602" 惟(N,q)=q+N-1q=(q+N-1)!q!(N-1)!

localid="1650337124840" 惟(4,2)=4+2-12=(4+2-1)!2!(4-1)!=10

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Most popular questions from this chapter

For a single large two-state paramagnet, the multiplicity function is very sharply peaked about N鈫�=N/2.

(a) Use Stirling's approximation to estimate the height of the peak in the multiplicity function.

(b) Use the methods of this section to derive a formula for the multiplicity function in the vicinity of the peak, in terms of x鈮�N鈫�鈭�(N/2). Check that your formula agrees with your answer to part (a) when x=0.

(c) How wide is the peak in the multiplicity function?

(d) Suppose you flip 1,000,000coins. Would you be surprised to obtain heads and 499,000 tails? Would you be surprised to obtain 510,000 heads and 490,000 tails? Explain.

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(a) How many different macro states are available to this system?

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(d) What is the probability of finding exactly half of the energy in solid A?

(e) Under what circumstances would this system exhibit irreversible behavior?

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