## V

Here, the system moves from state 1 to state 2 by the lower path and returns by the upper path. No matter what the shapes of these two trajectories, AU for the cycle 1 ^ 2 ^ 1 must be zero because U is a path-independent thermodynamic property. The form of the first law for the cycle, which follows from integrating Eq (1.12) with (bdU = 0, is:

where the integrals traverse the complete cycle. The cyclical work and heat depend on the path chosen but their path-integrals are always equal.

The forms of the First Law given by Eqs (1.4) and (1.7) apply to a system and do not involve the surroundings. However, the surroundings, which supply the Q to the system and receive W from it, must also obey the first law. The equation:

is at once the law of Conservation of Energy and a form of the First Law of Thermodynamics. As in Eq (1.4), kinetic energy and potential energy changes have been neglected in Eq (1.8).

Since AUsurr = Qsurr - Wsun, Eqs (1.4) and (1.8) imply that Q + Qsurr = W + W^. This equation does not mean that Qsurr = -Q and Wsurr = -W; these individual equalities hold only for reversible processes such as the compression of the ideal gas in Fig. 1.12.

System 1 |
System 2 |

## Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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