Generally, the first law of thermodynamics is referred to as another manifestation of the well-known law of conservation of energy. However, in thermodynamics it has a different significance as the law evolved from the observation that adiabatic work done in taking a system from an initial state to a final state of same bulk (potential and kinetic) energies is independent of the path and depends only on the properties of the initial and the final states. This sounds strange because in general work is path dependent and furthermore any property that depends only on the initial and final states (and not on the path) must represent some state function. We shall see how this leads to the thermodynamic concept of internal energy of a system.
Adiabatic Work between Two States of same Bulk Energies
A thermodynamic system may possess bulk potential and kinetic energies. For example, consider a fixed mass of a gas contained in a cylinder piston arrangement and carried in an airplane from one place to another. Taking the gas as our system, it has bulk potential energy due to the height of the airplane above the surface of earth and bulk kinetic energy due to its speed. If during the flight some operations are done on the gas, say it is compressed, the final and the initial states of the system are different but they have the same bulk energies. In the following we consider situations of this type.
It is known that a system may be taken from a given initial equilibrium state (that may have some fixed values of bulk kinetic and potential energies) to a final equilibrium state (having same bulk energies) in many different ways. On the P–v–T surface each equilibrium state is represented by a point and each process by a curve. In general the work done in reaching the final state starting from the same initial state depends on the path and has different value for each path.