The Principle of Conservation of Energy and the First Law of Thermodynamics are separate ideas in this theory. The Principle of Conservation of Energy states that energy cannot be created or destroyed. If energy seems to appear or disappear, then we can always find a new form of energy which accounts for the discrepancy.
Our statement of the First Law of Thermodynamics is based on that of Caratheodory:
The amount of energy transferred to or from a thermodynamic system in an adiabatic transition--measured by work done in the system's environment--depends only on the initial and final equilibrium states.
This statement characterizes adiabatic transitions as those in which the energy change in the environment is measurable entirely as mechanical work.
Suppose that any three equilibrium states are given. We may number the states 1, 2, and 3 so that the following adiabatic transitions exist: (P1,V1) to (P2,V2), (P2,V2) to (P3,V3), and (P1,V1) to (P3,V3). Let E12 be the energy transferred to the system in an adiabatic transition (P1,V1) to (P2,V2), and let E23 be the energy transferred to the system in an adiabatic transition (P2,V2) to (P3,V3). Then, by the first law, the energy E13 transferred to the system in an adiabatic transition (P1,V1) to (P3,V3) is given by
E13 = E12 + E23,
whether or not the system passes through the state (P2,V2).
Internal energyIt follows from the First Law, and from the principle of conservation of energy, that we may define an internal energy potential U for the equilibrium states such that U(P3,V3) - U(P1,V1) = E13.
It follows from the First Law, and from the principle of conservation of energy, that we may define an internal energy potential U for the equilibrium states such that U(P3,V3) - U(P1,V1) = E13.
A path in the set of equilibrium states through a succession of neighboring states is called a quasistatic path. For each quasistatic path we define the quasistatic work W by
W = Integral: (-P)dV,
where the integral is from an initial state (P1,V1) to a final state (P2,V2) along the path. The value of W depends on the path as well as on the initial and final states.
Also, for each quasistatic path we define the quasistatic heat Q by
U(P2,V2) - U(P1,V1) = W + Q.
Since the value of W depends on the path, but the value of U(P2,V2) - U(P1,V1) does not, it follows that the value of Q depends on the path.
Quasistatic work and quasistatic heat are properties of quasistatic paths. They must not be confused with mechanical work and heat transfer in real physical processes. However, mechanical work and heat transfer may be practically equal to W and Q in a real process that is practically quasistatic.
By R. H. B. Exell, 2001. King Mongkut's University of Technology Thonburi.
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