Chemical Thermodynamics: Path or State Function?

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Frances Docherty

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Frances Docherty 1 week, 1 day ago

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Created this as a copy of Path or State Function?.

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Select whether each of the following is a path function, a state function, or neither:

(a) Entropy - Gap 0.

(b) Work - Gap 1.

(d) Enthalpy - Gap 3.

(e) The time it takes to travel home from campus - Gap 4.

(f) Avogadro's number - Gap 5.

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A state function is defined as a property whose value does not depend on the path taken to reach that specific value.

A path function is defined as a property whose value does depend on the path taken from the initial to final state of the system it describes.

(a) The entropy of a substance is a state function as it is not dependent on the history of the substance - for instance, two identical tubs of water both at $\mathrm{20^\circ C}$ would have the same entropy, but one tub might have been heated up to $\mathrm{20^\circ C}$ from $\mathrm{5^\circ C}$ , whereas the other could have been cooled down to $\mathrm{20^\circ C}$ from $\mathrm{50^\circ C}$ ; the history of each tub (the 'path' it took to reach that temperature) is irrelevant, only the current state of the water is important for its entropy value.

(b) The work done by a body moving between two points is a path function as it is dependent on the path taken by the body between these two points, not the distance separating the two points. For instance, two cyclists could cycle from one end of a road to another, with one cycling directly along the road between the points, and another travelling off-road into a field, cycling in circles for a few minutes, then cycling back onto the road and to the destination - both cyclists have travelled between the same two points, but the off-road cyclist did much more work than the one who stayed on the road, so the work done has depended on the path taken between the points, not the distance separating the points.

(c) The internal energy of a system is a state function as it is not dependent on the history of the system; only the current properties of the system. This could be considered with the same water bucket example given for entropy - the history of the water would not determine its internal energy.

(d) The enthalpy of a system is a potential akin to internal energy, and is thus a state function.

(e) The time taken to travel home from campus is a path function as it is dependent on the path you take from campus to get back home - on a rainy day, you might decide to take the shortest and most direct route home to get out of the rain as soon as possible, and only take $\mathrm{25}$ minutes; whereas on a sunny day, you might decide to go for a walk in the park on your way home, and take $\mathrm{40}$ minutes.

(f) Avogadro's number is not a path function, as it does not depend on any system's history, but is also not a state function, as it is not really a property which can depend on anything - it's just a number.

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Chemical Thermodynamics: Path or State Function?

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Frances Docherty 1 week, 1 day ago

Frances Docherty 1 week, 5 days ago

Frances Docherty 1 week, 5 days ago

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