Entropy change quantitative meaning

The term entropy, which literally means a change within, was first used in 1851 by Rudolf Clausius, one of the formulators of the second law of thermodynamics. A rigorous quantitative definition of entropy involves statistical and probability considerations. However, its nature can be illustrated qualitatively by three simple examples, each demonstrating one aspect of entropy. The key descriptors of entropy are randomness and disorder, manifested in different ways. 

The second law of thermodynamics states that all spontaneous processes lead to an increase in disorder, which is quantitatively measured by means of the system s entropy, S. For an infinitesimally small process involving a flow of heat into the system, dq, the entropy change, d.S. is given by... 

Quantitative Meaning of the Entropy Change Two approaches for quantifying an entropy change look different but give the same result. The first is a statistical approach based on the number of microstates possible for the particles in a system. The second is based on the heat absorbed (or released) by a system. WeTl explore both in a simple case of 1 mol of an ideal gas, say neon, expanding from 10 L to 20 L at 298 K ... 

It is desirable to find some common measure (preferably a quantitative measure) of the tendency to change and of the direction in which change can occur. In the 1850s, Clausius and Kelvin independently formulated the second law of thermodynamics, and Clausius invented the term entropy S (from the Greek word TpoTT-rj, which means transformation), to provide a measure of the transformational content or the capacity for change. In this chapter, we will develop the properties of this function and its relationship to the direction and extent of natural processes as expressed in the second law of thermodynamics. 

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