Mathematical formulation of the first law of thermodynamics: (Relationship between internal energy, work and heat).
The internal energy of a system can be increased in two ways.
(i) By supplying heat to the system,
(ii) By doing work on the system.
Suppose the initial internal energy of the system = U1
If it absorbs heat q, its internal energy will become = U1 + q
If further work w is done on the system, the internal energy will further increase and become = U1 + q + w.
Let us call this final internal energy as U2.
Then U2 = U1 + q + w or
U2 - U1 = q + w
ΔU = q + w
This equation is the mathematical formulation of the first law of thermodynamics.