Third Law of Thermodynamics - Video Tutorials & Practice Problems
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1
concept
Entropy of Perfect Crystals
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Now the third law of thermodynamics states that the entropy of a perfect crystal is zero at absolute zero. Now, absolute zero is zero Kelvin, here, we're going to say a perfect crystal is just a solid with a regular and ideal internal atomic arrangement. So here we have a perfect crystal where all of its components perfectly align with one another. And we're gonna say here this happens again at a temperature of zero. Kelvin, it's frozen perfectly in place because the temperature is as low as it can get. There's no such thing as negative Kelvin. So this is the bottom of the temperature scale and because it's frozen in place, it can't move around. So there's only gonna be one type of arrangement, it can have the one pictured. So here we're gonna say it has one micro state. Now, if the temperature happens to be above zero, Kelvin, then the particles are not frozen perfectly in place. They're gonna wiggle around a little bit, move around a little bit. Here, we have this one in red could maybe move around a little bit. And now it's over here. And again, this happens when the temperature is above zero Kelvin because it can arrange itself in more than one way. You say it has more than one micro state. Now, micro states are just a number of possible energetic ways to arrange components, whether they be atoms, molecules or ions of a system, which represents our chemical reaction. Now, the third law thermodynamics is high theoretical, we can't achieve absolute zero here on earth and on average, the universe has a temperature of around two Kelvin. OK. But so this is saying that if we could obtain this absolute zero value, this was what would happen. It'd be like freezing a structure perfectly in place. The truth is even solids around us don't stay perfectly still. If you have a powerful enough microscope and you look at it, you would see that the molecules of even your cell phone would be vibrating in place. That's because the temperature around us is higher than zero. Kelvin. So keep this in mind when we talk about micro states and the third law of thermodynamics.
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example
Third Law of Thermodynamics Example
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Now here in this example question, it says all the statements are correct except the greater number of molecular motion. The greater number of possible micro states, that's true. A perfectly ordered system has more than one micro state. Remember if you're a perfectly ordered system, you're a perfect crystal. This happens at absolute 00. Kelvin, you're frozen perfectly in place. So you'd only have one micro state. So this statement here is false. Any system at a temperature above zero. Kelvin has a positive um change in entropy value. Yes, because above zero, you can arrange yourself in different ways. You can move around greater motion, greater movement means will be greater change in the change of your entropy. So this is true. Perfect crystal exhibits no mole, no emotion. That is also true. A perfect crystal is fro frozen perfectly in place at zero. Kelvin can't move around, can't rearrange itself. So it only has one type of arrangement one micro state. So out of all the options, only option B is false.
3
concept
The Boltzmann Equation
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1m
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So the Boltzmann equation is credited to the Austrian physicist Ludwig Boltzmann, where he related entropy to the number of micro states. Now, entropy uses the variable S micro states, use the variable capital W. Here, the Boltzmann equation says that the entropy of my system which is my chemical reaction equals K times your natural log Ln times your number of micro states. Here K equals your Boltzmann constant and it is 1.38 times 10 to the negative 23 joules per Kelvin. And again, capital W just represents the number of micro states. Here we would say that the greater number of the micro states, the greater the entropy. That's because more micro states means more freedom of motion, more movement, more arrangements, more chaos, more disorder. So this would mean an increase in our entropy. Now a micro state equal to one would mean I would plug in one here four W all of one is zero, which would mean at the end that my entropy is equal to zero, right? So keep this in mind, this is just a mathematical way to calculate the entropy of my system. If the number of micro states are known.
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example
Third Law of Thermodynamics Example
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49s
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Now consider a system with a total of three times 10 to the 26 number of micro states. What is the entropy of such a system? All right. So here we utilize the Boltzmann equation. So we'd say that the entropy of my system, the change in entropy of my system equals K times L and of W K represents my bolt mint constant which is 1.38 times 10 to the minus 23 joules per Kelvin. And then we'd see Ln of the number of micro states which is three times 10 to the 26. When we plug this in, this will give me 8.41 times 10 to the negative 22 joules per Kelvin. This will represent the change in the entropy of my given system.
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Problem
Problem
A brand new deck of cards which hasn't been shuffled yet, possesses only one arrangement. Another, older deck has been shuffled and possesses 8 × 1067 arrangements. Calculate and compare entropies of each deck.
A
deck 1 = 0, deck 2 = 2.158 × 10−21 J/K
B
deck 1 = 0, deck 2 = 9.371 × 10−22 J/K
C
deck 1 = 0, deck 2 = 9.371 × 1024 J/K
D
deck 1 = 0, deck 2 = 2.158 × 1025 J/K
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