Entropy Change For Ideal Gas

vii.1 Entropy Change in Mixing of Ii Platonic Gases

Consider an insulated rigid container of gas separated into 2 halves by a heat conducting partition so the temperature of the gas in each part is the aforementioned. Ane side contains air, the other side another gas, say argon, both regarded every bit ideal gases. The mass of gas in each side is such that the pressure is also the aforementioned.

The entropy of this system is the sum of the entropies of the two parts: $S_\textrm{system} = S_\textrm{air} + S_\textrm{argon}$ . Suppose the partition is taken away so the gases are free to diffuse throughout the volume. For an platonic gas, the energy is not a function of book, and, for each gas, at that place is no change in temperature. (The energy of the overall system is unchanged, the two gases were at the same temperature initially, and then the final temperature is the same as the initial temperature.) The entropy modify of each gas is thus the same as that for a reversible isothermal expansion from the initial specific volume to the terminal specific book, . For a mass of platonic gas, the entropy change is $\Delta S = mR\ln(v_f/v_i)$ . The entropy change of the system is

$\displaystyle \Delta S_\textrm{system} = \Delta S_\textrm{air} + \Delta S_\text... ...\textrm{argon}\ln\left(\frac{v_{f,\textrm{argon}}}{v_{i,\textrm{argon}}}\right)$

(vii..1)

Equation (7.1) states that there is an entropy increase due to the increased book that each gas is able to access.

Examining the mixing process on a molecular level gives boosted insight. Suppose we were able to come across the gas molecules in different colors, say the air molecules as white and the argon molecules equally red. After nosotros took the division abroad, nosotros would run across white molecules outset to move into the cherry region and, similarly, scarlet molecules start to come into the white book. Every bit nosotros watched, equally the gases mixed, there would be more and more of the dissimilar color molecules in the regions that were initially all white and all red. If we moved further abroad and so we could no longer pick out individual molecules, we would see the growth of pinkish regions spreading into the initially red and white areas. In the final country, we would expect a uniform pink gas to exist throughout the volume. There might be occasional small regions which were slightly more red or slightly more white, but these fluctuations would but last for a time on the order of several molecular collisions.

In terms of the overall spatial distribution of the molecules, we would say this terminal land was more random, more mixed, than the initial state in which the ruby-red and white molecules were confined to specific regions. Another style to say this is in terms of ``disorder;'' in that location is more disorder in the last state than in the initial state. One view of entropy is thus that increases in entropy are connected with increases in randomness or disorder. This link can be made rigorous and is extremely useful in describing systems on a microscopic basis. While we practice not have scope to examine this topic in depth, the purpose of this affiliate is to make plausible the link between disorder and entropy through a statistical definition of entropy.

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