What Is Entropy?
Is your bedroom usually tidy, or does it tend to stay messy? I'll bet that more often than not, your bedroom is junky rather than neat and clean. Don't worry - my room is the same way, and it's all due to entropy!
There is only one arrangement of your bedroom that has everything in its proper, designated place; however, there are many different arrangements of your room that will cause things to be out of place and disordered. Thus, the probability of your room being messy is much greater than its probability to remain neat and clean. Since nature spontaneously proceeds towards the highest probable arrangement, your room proceeds towards a state of messiness.
The measure of such randomness and disorder in the universe is called entropy. In chemistry, entropy is represented by the capital letter S, and it is a thermodynamic function that describes the randomness and disorder of molecules based on the number of different arrangements available to them in a given system or reaction.
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We know from our study of the properties of matter that molecules in the solid phase have a strict, rigid position; molecules in the liquid phase are closely packed but have the freedom to flow more freely than solid molecules; and molecules in the gaseous phase have no fixed position and are able to spread out and move around as freely as possible.
As you can see here, gas molecules have the ability to expand more so than molecules in any other phase. Thus, gas molecules have the highest positional entropy. Positional entropy depends on the number of available configurations or arrangements in space. Because gas molecules can expand and move around more freely, they have more possible arrangements, or positions, giving them greater entropy.
Moreover, since liquid molecules can move more freely than solid molecules, liquids have a greater positional entropy than solids. Overall, we see that entropy increases from the solid phase to the liquid phase and from the liquid phase to the gaseous phase.
Second Law of Thermodynamics
As we've learned so far, the nature of the universe is to move towards the most probable state available. In terms of entropy, this means that in any spontaneous process (a process that occurs without outside influence), there is always an increase in the entropy of the universe. This is known as the second law of thermodynamics, which, simply stated, declares that the entropy of the universe is ever increasing.
In summary, entropy is a thermodynamic function that measures the randomness and disorder of the universe. Positional entropy is based on the number of molecular positions or arrangements available to a system. Gas molecules have the highest positional entropy of any state of matter. While liquid molecules have a greater entropy than solids, both are much less than the entropy of gaseous substances.
Finally, every spontaneous process in the universe naturally moves towards an increase in entropy, which means the entropy of the universe is constantly increasing, and your room is most likely to be a mess! Now you have an excuse to give your mom the next time she lectures you about cleaning up!
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Suppose you have two blocks of copper, each of heat capacity Cv = 200. J/ (° K ). Initially, one block has a uniform temperature of 300 ° K and the other 310 ° K. Calculate the entropy change that occurs when you place the two blocks in thermal contact with one another, and surround them with perfect thermal insulation. Assume the process occurs at constant volume.
Since the blocks have equal heat capacities, a given quantity of heat transfer from the warmer to the cooler block causes temperature changes that are equal in magnitude and of opposite signs. The final equilibrium temperature is 305 ° K, the average of the initial values.
When the temperature of one of the blocks changes reversibly from T1 to T2, the entropy change is Δ S = ∫ dq/T = ∫ cv dT / T with limits of integration from T1 to T2.
The entropy change is cv ln T2 / T1.
For the cooler block, Δ S = 200 J K-1 ln 305/300 = 3.306 J K-1
For the warmer block, Δ S = 200 J K-1 ln 305/310 = -3.252 J K-1
The total entropy change is 3.306 J K-1 - 3.252 J K-1 = .054 J K-1
The sign of the entropy change is positive as predicted by the second law of thermodynamics for an irreversible process in an isolated system.
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Entropy in Chemistry: Definition & Law
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