What Does Function of State Mean in Thermodynamics?

[KingDaniel]

Homework Statement

I read the following in my Thermodynamics study notes from university but I don't quit fully understand it. Please explain this to me in layman's terms:

"U is a "function of state", and is thus a property of the system. Although ΔU is defined, Q and W cannot be separately calculated from knowledge of the initial and final states alone".

What does "function of state" mean? Also, please explain the rest of the quote.

Homework Equations

ΔU = Q + W[/B]

The Attempt at a Solution

 

[Kinta]

Homework Statement

I read the following in my Thermodynamics study notes from university but I don't quit fully understand it. Please explain this to me in layman's terms:

"U is a "function of state", and is thus a property of the system. Although ΔU is defined, Q and W cannot be separately calculated from knowledge of the initial and final states alone".

What does "function of state" mean? Also, please explain the rest of the quote.

Homework Equations

ΔU = Q + W[/B]

The Attempt at a Solution

To say that the potential energy U of a system is a "function of state" is to say that the value of U doesn't depend on the way in which the system's current state was arrived. In other words, you can relate it to potential energy changes in conservative fields. If you've already taken any course covering classical mechanics, you should know that the change in potential energy of an object in a gravitational field is path independent; it only cares about initial and final position. However, the total work done by someone (not the field) in moving said object in the gravitational field is path dependent and cannot be found with certainty by only looking at the initial and final positions of the object. Does that help?

 

[Chestermiller]

To say that the potential energy U of a system is a "function of state" is to say that the value of U doesn't depend on the way in which the system's current state was arrived. In other words, you can relate it to potential energy changes in conservative fields. If you've already taken any course covering classical mechanics, you should know that the change in potential energy of an object in a gravitational field is path independent; it only cares about initial and final position. However, the total work done by someone (not the field) in moving said object in the gravitational field is path dependent and cannot be found with certainty by only looking at the initial and final positions of the object. Does that help?

In the context that the OP is using, U is not potential energy. It is thermodynamic internal energy.

 

[KingDaniel]

@Kinta , it makes sense when I think about it in the context of potential energy...because say for example, the Work done in moving a block directly vertically up to a certain point would be different (greater) than the Work done in sliding the same block up a ramp to the same height. This is because the Work done depends on the "distance moved by the point of application of the force in the direction of the force", right?
However, please try to put it in thermodynamics context. @Chestermiller , please help too

 

[KingDaniel]

Also, if something is a "function of state" doesn't it mean that it it depends on the current state?

 

[Kinta]

In the context that the OP is using, U is not potential energy. It is thermodynamic internal energy.

You're right, @Chestermiller. I let my analogy get a little too far ahead of me and lost sight of the context.

@Kinta , it makes sense when I think about it in the context of potential energy...because say for example, the Work done in moving a block directly vertically up to a certain point would be different (greater) than the Work done in sliding the same block up a ramp to the same height. This is because the Work done depends on the "distance moved by the point of application of the force in the direction of the force", right?
However, please try to put it in thermodynamics context. @Chestermiller , please help too

The example I gave with potential energy and the interpretation of it you've given are still acceptable ways to think about what is meant by an "equation of state". The takeaway, though, is that an equation of state describes a quantity that doesn't care about the methods by which it reached its current state.

To put this in the context of your original post, imagine the following situation. Let's say I show you some gas in a container that is both compressible and temperature-variable (i.e., the container can be heated to add heat to the gas). By some sort of wizardy, I've ascertained the gas's thermal internal energy and I share that information with you. Now I tell you to leave the room and come back in about 5 minutes. When you come back, I inform you that the internal energy of the gas has changed by some known amount so that we have a value for the change in internal energy. If you're then asked, "By what method was the increase in thermal internal energy of the gas attained?", you'd be unable to give a certain answer because you wouldn't know if the gas was compressed or heated, but you'd still know the change in internal energy of the gas.

 

[Chestermiller]

@Kinta , it makes sense when I think about it in the context of potential energy...because say for example, the Work done in moving a block directly vertically up to a certain point would be different (greater) than the Work done in sliding the same block up a ramp to the same height. This is because the Work done depends on the "distance moved by the point of application of the force in the direction of the force", right?

Wrong. If the ramp is frictionless, the amount of work is the same. The distance is larger but the force is less. Their product is the same.

However, please try to put it in thermodynamics context. @Chestermiller , please help too

Please see my discussion of this topic in the Physics Forums insight article I wrote: https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/. Even though the title implies the 2nd law of thermodynamics, there is key discussion of the 1st law. The article addresses the very questions that you are asking.

Chet