Entropy (S): a measure of the dispersal of energy, as a function of temperature, in a system. To understand entropy, we need to consider probability. Think about a deck of cards…

Only one way to be ordered in sequence like a new deck. Improbable after shuffling Random order much more probable after shuffling Many ways to be out of sequence.

Note: probability is the likelihood of an event occurring. Spontaneous process: The gas atoms expand to occupy both flasks when the valve is opened. Why?? How is probability involved in this process? Note: probability is the likelihood of an event occurring. Let’s do an exercise involving dice to understand more about probability.

If your roll of two dice resulted in a score of 3, 4, 5, 6 or 7, please click now.

If your roll of two dice resulted in a score of 7, 8, 9, 10 or 11, please click now. (Yes, the 7’s get to answer both questions.) Note: depending on polling system being used, you may be able to gather the data directly. These questions work for multiple choice type clickers.

If your roll of two dice resulted in a score of 2, 7 or 12, please click now. (Yes, the 7’s get to answer again!)

Total probability = 1

Imagine there is only one atom. Let’s relate the concept of microstates and probability to entropy and chemical systems: Imagine there is only one atom. Two possible arrangements when the valve is opened. Probability is ½ that the atom will be found in the left bulb. Just as with the dice, each of the possible arrangements is called a microscopic state, or a microstate.

Now, add a second atom. There are now 4 possible arrangements or 4 microstates.

With three atoms there are 8 microstates. What is the relationship between the number of microstates, the number of positions and the number of atoms? number of microstates = nx where n = number of positions and x is the number of molecules

Consider the ways that 4 atoms can be arranged… # of microstates = 24 = 16 All 4 atoms in one bulb 2 possible configurations, or microstates

3 atoms in the left and 1 atom in the right 4 possible configurations, or microstates 3 atoms in the right and 1 atom in the left 4 possible configurations, or microstates

6 possible configurations, or microstates Two atoms in the right and two atoms in the left. 6 possible configurations, or microstates This distribution has the greatest number of microstates and is the most probable distribution.

On a macroscopic scale, it is much more probable that the atoms will be evenly distributed between the two flasks because this is the distribution with the most microstates.

Ludwig Boltzman related the number of microstates (W) to the entropy (S) of the system: S = k ln W where k = Boltzman constant = 1.38 x 10-23 J/K A system with fewer microstates has lower entropy. A system with more microstates has higher entropy.

The 2nd Law of Thermodynamics can be restated as follows: An isolated system tends toward an equilibrium macrostate with maximum entropy, because then the number of microstates is the largest and this state is statistically most probable.

Assign a value of +½ and a value of –½. Consider two spins. Assign a value of +½ and a value of –½. How many microstates are possible? 22 = 4 How many macrostates are possible? Probability +½ + +½ = 1 ¼ +½ + -½ = 0 ½ -½ + -½ = -1 ¼ Which macrostate is the most probable? +½ + -½ = 0 It is more probable to have a pair of electrons with unpaired spins than with paired spins.

Positional probability: depends on the number of positions in space (positional microstates) that yield a particular state. lower entropy greater entropy lower positional probability higher positional probability

Which distribution of 6 particles into three interconnected boxes has the highest entropy?

Odyssey simulation of states of matter

Select the correct statement: The solid state has lower positional probability and greater entropy than the gas state. The solid state has higher positional probability and greater entropy than the gas state. The solid state has lower positional probability and lower entropy than the gas state. entropy solid < entropy liquid < entropy gas

Ludwig Boltzman related the number of microstates (W) to the entropy (S) of the system: S = k ln W where k = Boltzman constant = 1.38 x 10-23 J/K A system with fewer microstates has lower entropy. A system with more microstates has higher entropy.

The use of entropy in predicting the direction of spontaneous change in states is in the Second law of thermodynamics: For any spontaneous process, the entropy of the universe, ΔSuniverse, increases.