# Entropy: Equation & Calculations

Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Entropy is the state of disorder or randomness of a system. Learn more about entropy and understand how to use the entropy equation through the example calculation. Updated: 10/27/2021

## What is Entropy?

Is it easier to make a mess or clean it up? That might seem like an odd question, and a pretty easy one to answer. But the answer to that question says a lot about how the universe works.

Entropy is disorder in the universe, measured in Joules per Kelvin. It's like the messiness of the universe. One consequence of the second law of thermodynamics is that entropy in the universe always increases. The best you could ever do is to keep the entropy of the universe the same, and even that would require a perfect, reversible process. That just doesn't happen in the real world. So, for all practical purposes, whatever you do will make the universe more disorderly.

Let's say I take a huge box of toy blocks. The bright-colored kind with the letters of the alphabet on one side, numbers on another, and a few pictures and symbols on the rest. Inside the box, they're neatly packed and in order. Then, I decide to pour them all over the floor. I have clearly just increased the entropy, the disorder in the universe. But then I pick them all up and put them back into the box, putting them all back in order. Great - so I've just broken the second law of thermodynamics and made the universe more orderly, right?

Well, not really. It was much harder to put the blocks back in order than it was to make the mess in the first place. While I was putting them back in the box, I was using energy in my muscles. When you do that, your muscles get hot, and thermal energy spreads out from your muscles to your body and eventually the outside world. The disorder created by that process is greater than the order you create by putting the blocks back. So, unfortunately, it's all for nothing.

You can never really decrease the entropy in the universe. We're doomed to witness the universe get more and more disorderly as it expands - energy spreading out forever and ever until it becomes a dark, low energy, terribly depressing place.

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## Entropy Equation

If you want to learn more about entropy, you can check out another video lesson on the topic. But, in this lesson, we're going to talk about how to do some entropy calculations.

When it comes to entropy, there is one really important equation - the equation for change in entropy: the change in entropy for a system, delta S, is equal to the heat transferred to or from that system, Q, measured in Joules, divided by the average temperature of that system, T, measured in Kelvin.

A few important things to note about this equation: since it's an energy divided by a temperature, that means your answer for the change in entropy will have the units Joules per Kelvin (Joules divided by Kelvin), and the temperature you plug in really does have to be Kelvin - if you plug in Celsius this equation won't work.

There's also a sign convention for this equation. A positive value of Q means the heat is being transferred into the system or object, where as a negative value of Q means the heat is being transferred out of the system or object. It's also worth noting that if your final entropy figure comes out as negative, meaning that the entropy of the object has decreased, then entropy must have increased elsewhere to compensate because, as I mentioned, the entropy of the universe must always increase.

Strictly speaking, the entropy equation only works for a reversible process, one where the entropy of the universe remains the same. In the real world, there's no such thing as a truly reversible process, but we can still use this equation to calculate the entropy change of a real-world process. That's because entropy change is what's called path independent. This means that the entropy change is the same, no matter how you get from the initial state to the final state.

If we know where a real-life system started, and we know where it ended, we can calculate the entropy change for a reversible process with the same start and end points, and the number will be exactly the same. It's like following a treasure map. In the end, it doesn't really matter how you get there, as long as you find the treasure. The result is the same.

## Entropy Calculation Example

Okay, let's go through an example. A bucket of hot water is placed in contact with a huge ice pack. This causes heat to spontaneously transfer from the hot water into the ice in an irreversible process. The ice pack has a temperature of 250 K, and the hot water has a temperature of 350 K.

Let's say that 5,000 J of heat transfers between them over a short time, but because the bucket and the ice pack are so large, it hasn't yet changed the temperature of either object. And you're asked to calculate the total change in entropy in the universe due to the 5,000 J transfer.

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