Entropy in Chemistry: Definition & Law

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LaRita Williams

LaRita holds a master's degree and is currently an adjunct professor of Chemistry.

Expert Contributor
Elaine Chan

Dr. Chan has taught computer and college level physics, chemistry, and math for over eight years. Dr. Chan has a Ph.D. in Chemistry from U. C. Berkeley, an M.S. Physics plus 19 graduate Applied Math credits from UW, and an A.B. with honors from U.C .Berkeley in Physics.

In this lesson, we'll define chemical entropy as a thermodynamic function, discuss positional entropy as it relates to the states of matter, and state the second law of thermodynamics. Updated: 07/12/2020

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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  • 0:03 What Is Entropy?
  • 1:01 Positional Entropy
  • 2:03 Second Law of Thermodynamics
  • 2:25 Lesson Summary
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Positional Entropy

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.

States of matter

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.

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Entropy Calculation


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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