Internal Energy and Entropy

Following is the mathematical statement of the first law of thermodynamics for a system, neglecting the changes in the mechanical (kinetic and potential) energy:

In this equation, Q is the heat added to the system; W, the work done by the system; and ΔU, the change in the internal energy.

The internal energy U can be visualized as the kinetic and potential energy of a substance or system at the atomic and molecular level [7], and is one of the fundamental thermodynamic properties. Significance of the internal energy is linked to the first law of thermodynamics. If no heat is supplied (or removed) from the system, then -ΔU = W; that is, there is a decrease in the internal energy manifests as the work done by the system. Conversely, if work is done on the system, and no heat is supplied or removed from it, the net result is an increase in the internal energy of the system.

As mentioned previously, the first law does not indicate the feasibility of extracting the work from the system. Another fundamental thermodynamic quantity, entropy, is needed for this purpose. Entropy, as defined and visualized by Clausius,³ is a measure of the transformation content (capacity to transform) of the system [2]. It was shown by Clausius that only those transformations in which a system experiences a loss in its capacity to transform can occur naturally or spontaneously. Mathematically, change in entropy is always positive in natural processes:

3. Rudolf Clausius, 19th-century German mathematician and scientist, was a major contributor to and one of the founders of the discipline of thermodynamics.

Here, S is the entropy. The subscript adiabatic indicates that the process occurs in absence of any heat (energy) exchange between the system and the surroundings. This is one of the most useful formulations of the second law of thermodynamics [5]. The second law is often presented with several alternative formulations, all of which are equivalent. The details of these formulations are beyond the scope of this book and are generally discussed in the engineering thermodynamics and chemical engineering thermodynamics courses.

The utility of the concepts of internal energy and entropy in devising solutions to the first type of problems described should be apparent at this point. If the change in the internal energy can be determined for a system, then the amount of work that can be obtained from the system can be calculated. The changes occurring in the system (and surroundings, if needed) can also be determined. The calculation of change in the entropy allows us to determine whether or not the proposed transformation of the system is feasible naturally.