Entropy (classical Thermodynamics) - Entropy Change in Irreversible Transformations

Entropy Change in Irreversible Transformations

We now consider inhomogeneous systems in which internal transformations (processes) can take place. If we calculate the entropy S₁ before and S₂ after such an internal process the Second Law of Thermodynamics demands that S₂ ≥ S₁ where the equality sign holds if the process is reversible. The difference S_i = S₂ - S₁ is the entropy production due to the irreversible process. The Second law demands that the entropy of an isolated system cannot decrease. The entropy production is always positive.

Suppose a system is thermally and mechanically isolated from the environment (isolated system). For example, consider an insulating rigid box divided by a movable partition into two volumes, each filled with gas. If the pressure of one gas is higher, it will expand by moving the partition, thus performing work on the other gas. Also, if the gases are at different temperatures, heat can flow from one gas to the other provided the partition allows heat conduction. Our above result indicates that the entropy of the system as a whole will increase during these processes. There exists a maximum amount of entropy the system may possess under the circumstances. This entropy corresponds to a state of stable equilibrium, since a transformation to any other equilibrium state would cause the entropy to decrease, which is forbidden. Once the system reaches this maximum-entropy state, no part of the system can perform work on any other part. It is in this sense that entropy is a measure of the energy in a system that cannot be used to do work.

An irreversible process degrades the performance of a thermodynamic system, designed to do work or produce cooling, and results in entropy production. The entropy generation during a reversible process is zero. Thus entropy production is a measure of the irreversibility and may be used to compare engineering processes and machines.