Heat content as a state function?

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Discussion Overview

The discussion revolves around the concept of heat content and whether it can be considered a state function. Participants explore the implications of heat content being path-dependent versus being a state variable, referencing a video and a PV diagram to illustrate their points.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the nature of heat content, suggesting that if heat is added in a cycle, it should not affect the heat content at a specific point, implying it cannot be a state variable.
  • Another participant agrees with the initial claim, explaining that heat content varies based on the path taken between states on a PV diagram, thus reinforcing the idea that it is path-dependent.
  • A clarification is provided regarding the term "cusps," which are described as points where the direction of a curve changes abruptly, relevant to the discussion of the PV diagram.

Areas of Agreement / Disagreement

Participants generally agree on the notion that heat content is path-dependent and cannot be classified as a state variable, though the discussion includes clarifications and questions about terminology.

Contextual Notes

The discussion relies on the definitions of state variables and path-dependent quantities, and the implications of these definitions are not fully resolved. The reference to the PV diagram and the specific video may introduce additional context that is not fully detailed in the posts.

firecool
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at 3:30 he introduces heat content to show why it can't be a state variable. he says that if q=2 is added to the cycle everytime you go around the cycle the heat content would be incremented by 2. but as heat=work shouldn't that extra 2 be lost as work and at point 1 you always have hc=5? watch the video to make sense of my question.. :)
 
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He's absolutely correct.

Another way to look at it. There are two cusps on that PV diagram connected by two different curved paths. Suppose the heat content of the point on the left is 5. What is the heat content of the point on the right? You will get a different answer for the upper path versus the lower one. You can't assign a heat content as a state variable to that point on the right because this supposed heat content depends on the initial state, the final state, and the path followed from the initial state to the final state. It is a path-dependent quantity.

A state variable, by definition, cannot depend on how the system attained its current state. A state variable is a function of the current state only.
 
cusps? :P
 
Cusp: "A point at which the direction of a curve is abruptly reversed". Or a bit more generally, a point at which the gradient to the curve doesn't exist. There are two "cusps" in that PV diagram in the video, one on the left and one on the right.
 
thanks! :)
 

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