Entropy and the Second Law

There were some contradictions in Carnot s work—a result of his reliance on the caloric theory—that were subsequently cleared up by Clausius. Clausius accepted Carnot s proposition that some heat must be thrown away when converting heat to work as a law of nature, something that cannot be proved or derived from something else, but as far as we have ever been able to tell describes the way the world works. He called it the second law of thermodynamics and then sought to recast it in a different, more general, form that did not apply to heat engines alone. He showed that an equivalent statement of the 

Accordingly, we now have a mathematical definition of entropy and the idea that it determines the direction of irreversible processes (heat flows from a hotter to a colder ). But 

Finally, we need to remind you about free energy. In many of our discussions we will be trying to establish whether or not a process will occur spontaneously— will this polymer dissolve in that solvent , for example. Conceptually, this is easily done, because once a system reaches equilibrium, its entropy is a maximum, so all we need to do is calculate if the entropy change for that process is positive. This is not so easily done for real systems, however, because they are not isolated from their surroundings. Dis- 

In summary, we have identified two basic types of spontaneous physical process  

To make progress with our quantitative discussion of bioiogical stmcture and reactivity, we need to associate the dispersai of energy and matter with the change in a state function. 

The measure of the disorderly dispersal of energy or matter used in thermodynamics is called the entropy, S. We shall soon define entropy precisely and quantitatively, but for now all we need to know is that when matter and energy disperse in disorder, entropy increases. That being so, we can combine the two remcuks above into a single statement known is the Second Law of thermodynamics  

The isolated system may consist of a system in which we have a specicd interest (a beaker containing rejigents, a biologiccd cell, or even cm orgcmeUe within a cell) and that system s surroimdings the two components jointly form a httle universe in the thermodynamic sense. 

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Entropy and the Second Law of Thermodynamics (Frame 2) provide us with a way of deciding whether a given process or reaction is spontaneous. 

The Entropy and Irreversible Processes.—Unlike the internal energy and the first law of thermodynamics, the entropy and the second law are relatively unfamiliar. Like them, however, their best interpretation comes from the atomic point of view, as carried out in statistical mechanics. For this reason, we shall start with a qualitative description of the nature of the entropy, rather than with quantitative definitions and methods of measurement. 

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