The First Law Interrelates Heat, Work, and Energy

The First Law of thermodynamics relates a change in energy, dU, to increments of heat 6q and work 5w  

The use of 5 as a differential element indicates that heat and work are path-dependent quantities, while the use of d indicates that their sum, the internal energy dU, is a state function (see pages 73-77). The signs of the quantities in the First Law are defined so that the internal energy increases when heat flows into a system, Sq 0, and when work is done on a system, diu 0. Energ is a property of a system while heat and work are properties of a process of energy transfer across a boundary. 

The First Law gives a way of relating w, a path-dependent quantity, to U, a state function. If you surround a working device with an insulating (adiabatic) boundary (6q = 0) it follows from the First Law that dU = Sw. The point is to determine a change AU from an experimentally measurable quantity, the work done on the system. In the lake analogy you could cover the lake with a tarp 

which is path-dependent, is related to the entropy, a state function, for quasi-static processes, as shown below.  

Combine the First Law and the Fundamental Energy Equation to Eind the Entropy 

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