The first law of thermodynamics is supported by a vast number of experiment ; no exceptions have been observed. Consequently, We accept it as a law of nature.We deduce many results from it and use it in innumerable applications.Notice that it is an empirical law, base on induction from experimental observations.It has not been proven.
The relationship between heat and work has shown using only cyclic Processes. Using cycles eliminates any possibility that the relationship been is influenced by net changes in the system. In the next section,we see what happens when the process is not cyclic