The internal energy (U) is a state function i.e., when a process occurs, the change in its value depends only upon its initial state and final state and is independent of the path by which the change is brought about.
For example, let us consider a system having a particular pressure, volume and temperature is represented by point A in the following figure. Now, let, the pressure, volume, and temperature are changed in such a way that the system is brought to point B by path-I. Now, if the system is returned to point A by path-II, then the energy change involved in the path-I must be equal in magnitude to that involved in path II. If the energy changes involved in paths-I and II are not the same, then suppose that the increase in internal energy by path-I is greater than the decrease in internal energy along path-II.
Thus, by carrying out the process A to B () by path-I, and the reverse process B to A () by path-II, though the original state has been restored, some energy has been created. This is contradictory to the first law of thermodynamics. Thus, it may be concluded that the energy change involved in the process A to B () must be equal in magnitude to that involved in the reverse process B to A (). In other words, the energy change accompanying a process is independent of the path followed and depends upon the initial and final states only. Thus, if UA is the internal energy of the system in the initial state and UB that in the final state, then the change in internal energy accompanying the process would be given by UB – UA. Therefore, the internal energy is a state function and change in internal energy is a perfect or exact differential.
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