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Chapter 2: Q.2.8 (page 59)

Consider a system of two Einstein solids, \(A\) and \(B\), each containing 10 oscillators, sharing a total of 20 units of energy. Assume that the solids are weakly coupled, and that the total energy is fixed.

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

(b) How many different microstates are available to this system?

(c) Assuming that this system is in thermal equilibrium, what is the probability of finding all the energy in solid \(A\) ?

(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?

Short Answer

Expert verified

(a) 21 macrostates are available

(b) Ωoverall=6.892×1010microstates are available

(c) the probability that all the energy is in solid Aat thermal equilibrium,P=1.453×10-4

(d) the probability in this case isP=0.1238

Step by step solution

01

find macrostates and microstates 

Suppose we have two systems of Einstein solids, Aand Bwith NA=NB=10and qA+qB=20

(a) the number of macrostates is therefore:

q+1=20+1=21

because we start counting 0 to 20.

(b) the number of microstates formula is given by:

ΩoverallNoverall,qoverall=qoverall+Noverall-1qoverall=qoverall+Noverall-1!qoverall!Noverall-1!

where,

qoverall=qA+qB=20,Noverall=NA+NB=20

so,

width="385">Ωoverall=20+20-120=(20+20-1)!20!(20-1)!=6.892×1010

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Most popular questions from this chapter

Fill in the algebraic steps to derive the Sackur-Tetrode equation(2.49).

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