Consider a system undergoing the changes depicted in Fig. 2.21. The initial state of
the system is i and in this state the internal energy is Ui. Work is done by the system
as it expands adiabatically to a state f. In this state the system has an internal energy Uf
and the work done on the system as it changes along Path 1 from i to f is w. Notice our
use of language: U is a property of the state; w is a property of the path. Now consider
another process, Path 2, in which the initial and final states are the same as those in
Path 1 but in which the expansion is not adiabatic. The internal energy of both the
initial and the final states are the same as before (because U is a state function).
However, in the second path an energy q′ enters the system as heat and the work w′ is
not the same as w. The work and the heat are path functions.