What is Entropy? – Definition, Law & Formula

In this lesson, you will learn the definition of entropy and discover how it can be applied to everyday situations. You will explore the second law of thermodynamics which is where entropy is introduced, and you will examine the formula for entropy and find out how to use it in a variety of instances.
What Is Entropy?
Let us say you have a bag of balls. You grab one ball from the bag and put it on the table. How many ways can you arrange that ball? The answer: one way. What if we grab two balls and ask the same question? Now there are more ways to arrange the two balls. We keep doing this until all the balls are on the table. At this point, there are so many ways to arrange the bag of balls, you might not even be able to count the number of ways. This situation is very much like entropy.

In this situation, entropy is defined as the number of ways a system can be arranged. The higher the entropy (meaning the more ways the system can be arranged), the more the system is disordered. Another example of this definition of entropy is illustrated by spraying perfume in the corner of a room. We all know what happens next. The perfume will not just stay in that corner of the room. The perfume molecules will eventually fill up the room. The perfume went from an ordered state to a state of disorder by spreading throughout the room.

This image shows molecules represented by blue circles initially in an ordered state within the spray bottle, but once they are sprayed out you can see they enter a disordered state.
entropy spray bottle example
How Entropy Increases
According to the second law of thermodynamics, in any process that involves a cycle, the entropy of the system will either stay the same or increase. When the cyclic process is reversible then the entropy will not change. When the process is irreversible, then entropy will increase. The best way to describe a reversible process is to describe watching a movie. If you can’t tell if the movie is playing forwards or backwards, then the process is reversible. However, if you can tell that the movie is playing in reverse, then the process is irreversible. For example, frying an egg is irreversible, as is blowing up a building. If you make a movie of these processes, you can tell forward from reverse. A simple example of a reversible process is changing the phase of something like melting a piece of metal and vice versa. The changes are only physical, therefore, they are reversible. If you make a movie of it, you will not be able to tell forward from reverse. Most microscopic processes are reversible.

The top image shows a reversible process because solid metal can be melted and then cooled down to form solid metal again. The bottom image is an irreversible process because once an egg is fried it can never be a raw egg again.
molten metal reversible process example and the fried egg irreversible process example
Change in Entropy Equation
If the process is reversible, then the change in entropy is equal to the heat absorbed divided by the temperature of the reversible process. In the equation, Q is the heat absorbed, T is the temperature, and S is the entropy.

change in entropy equation
Entropy is also the measure of energy not available to do work for your system. The higher the entropy, the less energy is available in your system to do work. When the system reaches equilibrium, the entropy reaches a maximum value, then the system is unable to do work. If the system was a living being, the living being would be dead in a state of maximum entropy.

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