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Problem 6

The diagram shows four states of a system, each with different internal energy, $E$ . (a) Which of the states of the system has the greatest internal energy? (b) In terms of the $\Delta E$ values, write two expressions for the difference in internal energy between State A and State B. (c) Write an expression for the difference in energy between State $\mathrm{C}$ and State D. (d) Suppose there is another state of the system, State E, and its energy relative to State A is $\Delta E=\Delta E_{1}+\Delta E_{4}$ . Where

would State $E$ be on the diagram? [ Section 5.2$]$

Answer

a)the state B of the system has greatest internal energy.

b) $$ \begin{array}{l}{\Delta E=\Delta E_{1}+\Delta E_{2}} \\ {\Delta E=\Delta E_{3}+\Delta E_{4}}\end{array}

$$

c) $\Delta E=\Delta E_{1}-\Delta E_{3}$

d) the state E will be placed above on the state

in the diagram.

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## Discussion

## Video Transcript

All right, guys, we're gonna be doing problem number six in chapter five. The chemistry, the central science. So you can see in the question of diagram shows for state to beach system, each with different internal energy party. They wonder which of the state's has the greatest internal energy value. And that will be stayed b at as that we'LL have the highest Colonel Andry since the change in energy to state be from the other states. It's positive. In a diagram with in the diagram, the states with the highest internal energy are closer to top. As it says as on the side of the diagram, let me just write down the answer to a is going to be state be since its senses, that topped the diagram and has, as you have positive change in energy, that it's going to be state state. He's going to have our highest energy value as Delta is Graydon zero. So we have state be he as our answer now in Part two and part B, as in turns the IV eyes with two expressions for a different in internal energy state between state day and state. Be yes, us. So we're gonna be ready. And two Best two expressions. So we're going to that We're going to be converted simply. Is this so we're doing an aide to be transition different. So we're going to use so we can write this as simply as Delta IV one. Let's Delta E too. So the reason we're running it like this Is that the sum of these changes? Yes. Based on some of the changes we get the total total change our energy. Now, we can also write this as this for expression, too. We can write this as Delta eat Delta Eat three, plus Delta eighty four. So these were two expressions we can write for different term energy between between State day and state. Be because remember, the reason we add is because we get we get the total change in the energy So we get changed from from basically I say we get the change energy between two points and then the change org Another two points. We had those together and I'll give a stage and between and b so think of it this way. We're going from point A to point B. Now we can write that as yes. Now let's put a point in the middle. It's a this is point C. So we're going from point A to point C that from Point C too wouldn't be now. We would add the distance from on ABC and add that the distance from from sea to be and adding those together give her overall change from A to B. Now for part B. They want to run expression of a difference between energy states, D. C and D. So so for this one, we're going to write C to D transition as Delta lto Eat three minus Delta E. One. So this is because we subtract. We don't get a perfect path from C to D. So we need to get the difference from So we're doing basically this kind of thing where we have our path path from eighty eighty d, and we should attract that by a path from A to C, and that gives us our D to see transition. So let's say we have this kind of thing. Think so. This is and against from color, So just a better visualize it, Does it think about it, Think about it like this this is our is going to be a eh This is going to be D and this is going to be C So we have to transitions a to C and A to D table. If I got reverse these this should be they should be C and this should be be so there's going to be C and that's going to be D that we're going us. So we're going to We can basically think of this as as a tea minus a to C. See. So we have our ADA di transition with this large blue line and then we subtract, we subtract the difference from our agency transition and that allows us to get our C to D transition now for part D. They want us to suppose there's in their system when our state of the system state E and Haringey relative to state A is he don't tease equal to one plus four. Where would say e. B on the diagram? Yes, yes. So let's see s So let's put this in first. Delta E is equal to have Delta E one. Listen, Delta tell Teo e too. Sorry, not Delta e to Delta Delta e for So Delta E for is greater than Delta is greater than Delta E too. Since they're both added to the one the value continually for the greatest and the highest on the diagram, this would be above this would be above stick. This would be this would be a bust, a B. And since they'd be, we saw here us. We see the transition from A to B and since for the transition from this transition, is that it be is e one plus e to and saying he is e one plus before state, he would be the highest on diagram and be above of state be so So let me just write this. So I'm going to write it as B B is equal to Delta e of the e one plus Delta e too to and E is going to be equal to I doubt he'ii one plus Delta T for For and since eat. Lt Ford's greater than Delta eighty three is going to be higher than be

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