In the First law of thermodynamics, we say dE=dQ-dW ; we say dQ and dW are not state functions because their value depends upon path taken. My query is, how to physically interpret this statement?? What are various paths ( one or more illustrative example(s) will be helpful).Thanks!!
d'Q and d'W are not total differentials. So when you integrate them it is not just simple definite integrals. Interval of integration is replaced by a certain curve connecting two points on the plane or in the space.
Path dependency means, usually, some irreversible process is involved; hence, friction and other dissipation forces would cause the path integrals to deviate from a simply connected space. If the process is reversible, that is to say, there is no friction or other lossy influences, then the path integrals are State Functions. Adiabatic processes are reversible processes, hence, are described by State Functions.
The issue concerning state functions vs non-state functions in thermodynamics is problematic for most students, particularly with engineering students who study fluid mechanics, heat transfer etc.. This is because the connection between continuum mechanics and thermodynamics is not adequately discussed. I have attached some notes that I use to illustrate the key connections between these two subject groups. Typically this should be done at the graduate level, but a watered down version can also be used at the advanced undergraduate level in engineering. The appendix of these notes addresses exact functions.
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