Classical Mechanics
# Statistical Thermodynamics

We mix \( 700 \text{ ml} \) of a \( 6 \% \) solution of salt in water and \( 700 \text{ ml} \) of a \( 4 \% \) solution of sugar in water. At equilibrium, how much salt is in \( 700 \text{ ml} \) of the mixture solution?

**Note**

- \(X\)% indicates percent weight by volume. For example, 200 mL of a \(2\)% fructose solution contains 4 g fructose.

There are three boxes with red and white balls. The first box contains a total of \(200\) balls: \( 80 \) white balls and \( 120 \) red balls. The second box contains \( 400 \) balls, and we mix them with the \( 200 \) balls in the third box. Then we re-divide those mixed balls between the second and third boxes, \( 400 \) and \( 200 ,\) which are exactly the original numbers. Now, we conduct the same kind of mix-and-divide process with the third and first boxes, and find that there is no change in the ratio of red and white balls in the first box. How many red balls are in the second box?

**Assumption**

- Whenever we conduct the mix-and-divide process on any two boxes, the resulting ratio of white and red balls in each box is the same, which is true on average.