Vanishing of a cyclic integral the property of a state function?

In summary, a state function is defined as something whose integral is independent of the path taken for the integral. This is a concept in thermodynamics. Therefore, the vanishing of a cyclic integral is a property of a state function since it can be split into two paths that cancel each other out. This also explains why state functions are path independent.
  • #1
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Why is the vanishing of a cyclic integral the property of a state function?
 
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  • #2
as far as i can tell, a state function is required to be something whose integral is independent of the path chosen for the integral, this is from searchign with google, and appears to be a thermodynaics thing. if we assume this is the definition of a state function then it is clear why any integral over a loop is zero since we may split the loop into two parts and consider the loop as a path from A to B followed by a path from B to A and the integral over a path from B to A is minus the integral we get if we went along that path backwards so they must add up to zero.

if you're asking why state functions are path independent then could i have your definition of state function.
 
  • #3
Thank you~ I understand now.
 

Related to Vanishing of a cyclic integral the property of a state function?

1. What is the vanishing of a cyclic integral and why is it important in science?

The vanishing of a cyclic integral refers to the property of a state function in thermodynamics where the integral of a closed loop process is equal to zero. This is important because it allows for the determination of the change in a state function without having to know the specific path taken.

2. How is the vanishing of a cyclic integral related to the first law of thermodynamics?

The vanishing of a cyclic integral is directly related to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted. This property allows for the accurate calculation of energy changes in a system.

3. Can you provide an example of a cyclic integral in a real-life scenario?

One example of a cyclic integral in a real-life scenario is the Carnot cycle, which is a thermodynamic cycle used in heat engines. In this cycle, the vanishing of the cyclic integral allows for the calculation of the efficiency of the engine.

4. What other fields besides thermodynamics use the concept of a cyclic integral?

The concept of a cyclic integral is also used in fields such as economics, finance, and physics. In economics, it is used to calculate the work done on a system, while in finance it is used to measure the net gain or loss in a portfolio. In physics, it is used to calculate the work done by a conservative force.

5. What are the limitations of using the vanishing of a cyclic integral in calculations?

While the vanishing of a cyclic integral is a useful property in state function calculations, it is important to note that it is only applicable to closed loop processes. If the process is not cyclic, this property cannot be used. Additionally, it only applies to state functions and cannot be used for non-state functions.

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