The internal energy as a state function

More precisely, the constant-volume heat capacity is the partial derivative of the function U with respect to the variable T, denoted as 

For more detail about partial derivatives, see Mathematical toolkit 8.1. 

The altitude is a state property because it depends only on the current state of the system. The change in the value of a state property is independent of the path between the two states. 

For example, the difference in altitude between the initial and final states shown in the diagram is the same whatever path (as depicted by the red and white lines) is used to travel between them. 

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Hosoya266 has discussed implications of graph-theoretical techniques and the Coulson-Longuet-Higgins atom-atom polarizability in an analysis of -electron networks. The internal energy as a state function of the polarizability volume and the diamagnetic susceptibility has been discussed by deVisser.265... 

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