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03:06
Manhattan College

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Problem 30

Indicate which of the following is independent of the path by which a change occurs: (a) the change in potential energy when a book is transferred from table to shelf, (b) the heat evolved when a cube of sugar is oxidized to $\operatorname{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g),(\mathbf{c})$ the work accomplished in burning a gallon of gasoline.

a) change in potential energy of the book is independent of the path.
b) Thus, the heat evolved by the oxidation of sugar cube to form $\mathrm{CO}_{2}(\mathrm{g})$ and $\mathrm{H}_{2} \mathrm{O}(g)$ is dependent on the path.
c) the work accomplished in burning of gasoline is dependent on the path.

## Discussion

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## Video Transcript

from number thirty in Chapter five. Chemistry is not a science one knows which is which of the phones independent a path which a change occurs. So part A that wants no the change in potential energy when it book is transferred from table to a shelf. Now, remember, the formula for potential energy energy is going to be hail to you is equal to MGH. So oh, you can think of the tension ideas like a as as it's proportional to the masher using it's proportional to the force of gravity you have and proportional to the height, the height you have from the ground. So a system that had So it's a state function function. It's independent of the path that that using, Let's say, I'm as whether I'm putting it directly from the tape table to the shelf or whether I'm putting it from the table, lifting up halfway in the air and then putting it on the shelf that the potential energy of your system system. The change in the contracting system is the same because you're because the overall change in the heights shirt, your role change in the height ofyours right of your of your book relative to the ground stays stays the same. Same. So now? No, this is going to be as there's going to be a yes now. Herbie, we're looking at the heat of Baldwin. When a Cuba sugar's oxidized to heal, too and issue a gas Well, no, us. He is not a state function. So you're not us. He does not say function, so it is not independent of path at the amount of heat you produced from this from this reaction that is going to depend on the specifics on the specific steps that you're taking thing and and those are very important not to confuse he will handle. The entropy is a state function. Heat, however, is not. So. This is going to be unknown. Never see the work accomplishing Bernie a gallon of gasoline. The answer is no, because it's going to depend on a lot of factors like, for example, how thoroughly the gasoline was burned burns. So So there may be That's right. This there there may be multiple. There multiple things that can affect whether or not not get your gasoline is going to be burnt. That whether or not your gasoline is going to be burned thoroughly, thoroughly, and that can affect the amount of work that your that your sister bet your system is doing. So work. So work is not going to be a state function, so it's not going to be independent of the independent of path. So that's it. That's a no here.