One mole of an ideal gas, so here are the gas In our first situation, we're starting off with The change in entropy for a number of different situations. Of either matter or energy, that really relates to a decrease in the number of available microstates, which means a decrease in And if we think about aĭecrease in the disorder of the system or an increase in the order, or a decrease in the dispersal Terms as meaning an increase in the number of microstates and therefore an increase in However, when we're using the equationĭeveloped by Boltzmann, we should think about these ![]() Using the word microstates, people will describeĪn increase in entropy as an increase in disorder or an increase in the dispersal Microstates decreases, that represents a decrease Of a system increases, that represents an increase in entropy, and if the number of According to this equation, entropy, symbolized by S, is equal to Boltzmann's constant, k, times the natural log of W, and W represents the number Now that we understand theĬoncept of microstates, let's look at an equationĭeveloped by Boltzmann that relates entropy to Is a number that's too high for us to even comprehend. So the number of microstatesĪvailable to this system of one mole of gas particles Moving from one microstate into another, into another, into another. The microscopic level, we see that the system is So from a macroscopic point of view, nothing seems to change. A good way to think aboutĪ microstate would be like taking a picture of Microscopic arrangement of positions and energies So going back to our boxes,īox 1, box 2 and box 3, each box shows a different To the kinetic energies of the particles. With an ideal gas here, by energies, we're referring Microscopic arrangement of all of the positions andĮnergies of the gas particles. Of each particle is equal to 1/2 mv squared, where m is the mass of each Particles are meant to represent the velocities of the particles. And the magnitude and theĭirection give a velocity. However, when we put anĪrrow on each particle, that also gives us the direction. Of a particle tells us how fast the particle is traveling. Slightly different positions and the velocities might have changed. Particles in our system at one moment in time, in box 1, if we think about them atĪ different moment in time, in box 2, the particles might be in Slamming into each other and transferring energy from Slamming into the sides of the container and maybe Here in the first box, imagine these gas particles ![]() However, from a microscopic point of view, things are changing all of the time. So from a macroscopic point of view, nothing seems to be changing. Particles is at equilibrium, then the pressure, the volume, the number of moles, and the temperature all remain the same. Moles at a specific pressure, volume, and temperature. And to think about microstates, let's consider one mole of an ideal gas. ![]() ) The most disorderly possibilities are also the most likely, with 20 out of 32 possibilities for the 3 heads and 2 tails and its reverse.Of entropy is related to the idea of microstates. The most disorderly possibilities are 3 heads and 2 tails and its reverse. ) They are also the least likely, only 2 out of 32 possibilities. (They are more structured than the others. The two most orderly possibilities are 5 heads or 5 tails. Otherwise, the analysis will be erroneous. Note that all of these conclusions are based on the crucial assumption that each microstate is equally probable. For example, 4 heads and 1 tail instance may occur on 5 different configurations, with any one of the 5 coins showing tail and all the rest heads. The following table shows all possibilities along with numbers of possible configurations (or microstate a detailed description of every element of a system). On the large scale, we are concerned only with the total heads and tails and not with the order in which heads and tails appear. What are the possible outcomes of tossing 5 coins? Each coin can land either heads or tails. This result, which has general validity, means that the total change in entropy for a system in any reversible process is zero.
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