Classical Mechanics

Statistical Thermodynamics

Equilibrium

         

603600 603600 gas particles are floating in a room. At equilibrium, walls are inserted into the room to divide the room into 3 3 equal parts. About how many particles are there in each divided room?

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

Note

  • XX% indicates percent weight by volume. For example, 200 mL of a 22% fructose solution contains 4 g fructose.

System A A , consisting of 22 22 particles, has total thermal energy E1=88 J. E_1 = 88 \text{ J}. System B B, consisting of 11 11 particles, has total thermal energy E2=44 J. E_2 = 44 \text{ J}. If system A A can exchange heat with system B B , what is the thermal energy of each particle at equilibrium?

There are three boxes with red and white balls. The first box contains a total of 200200 balls: 80 80 white balls and 120 120 red balls. The second box contains 400 400 balls, and we mix them with the 200 200 balls in the third box. Then we re-divide those mixed balls between the second and third boxes, 400 400 and 200, 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.

Particle A A with thermal energy E1=26 J E_1 = 26 \text{ J} is placed in a box with particle B B with thermal energy E2=8 J. E_2 = 8 \text{ J}. At equilibrium, what is the average thermal energy of both particles?

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