A system has three macrostates. Macrostates 1 and 3 are least likely and have one basic state each. Macrostate 2 is the equilibrium state and is three times more likely to occur than either of the other two macrostates.
Part A) What is the probability that the equilibrium state 2 occurs?
Part B) What is the probability that microstate 1 or 3 occurs?

Respuesta :

Answer:

a) 0.6

b) 0.4

Explanation:

The number of states available in macrostate 1 = 1 basic state

The number of states in macrostate 3 = 1 basic state too

But the number of states of macrostate 2 = 3 × (number of states in either of the macrostate 1 or 3) = 3 × 1 = 3

Total number of states available in the macrostates = 1+3+1 = 5

a) probability that the equilibrium state 2 occurs = (number of states available in equilibrium 2)/(total number of states) = (3/5) = 0.60

b) probability that microstate 1 or 3 occurs = (number of states available in microstate 1 or 3)/(total number of states) = 2/5 = 0.4

A) The probability that the equilibrium state 2 occurs is; 0.6

B) The probability that microstate 1 or 3 occurs is;

0.4

We are given;

  • Number of states available in Macrostate 1 = 1 basic state
  • Number of states in Macrostate 3 = 1 basic state

Now, Microstate 2 is 3 times more likely to occur than either of Microstate 3 or 1.

Thus;

Number of states in Macrostate 2 is;

3 × 1 = 3

Total number of states available in Macrostates 1, 2 and 3;

1 + 3 + 1 = 5

A) Probability that the equilibrium state 2 occurs is;

P(eq 2 occurs) = (number of states available in equilibrium 2)/(total number of states)

P(eq 2 occurs) = (3/5) = 0.6

B) Probability that microstate 1 or 3 occurs is;

P(eq 1 or 3 Occurs) = (Number of states available in microstate 1 or 3)/(total number of states)

P(eq 1 or 3 Occurs) = 2/5 = 0.4

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