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Line 79: − + − <center><big><math> \delta S_{rev} = Q/T </math></big></center>+ − Where <math>\delta S_{rev}</math> is the small change in entropy caused by a reversible process, <math>Q</math> is the added heat, and <math>T</math> is the absolute temperature. This increase in entropy must be at least <math>q/T</math>, but the entropy change itself <math>\delta S</math> is always greater.+ + + + + + + + + + + + +
→Second Law of Thermodynamics: Preliminary definition of entropy. To be continued on the other page.
{{cquote|No process is possible whose sole result is the complete conversion of heat into work}}
{{cquote|No process is possible whose sole result is the complete conversion of heat into work}}
What it meant was heat transfers to cooler temperatures, and not the other way around, which led to the concept of entropy. An idealised formula for an increase in entropy when heat is applied reads:
What it meant was heat transfers to cooler temperatures, and not the other way around. But this was still just a carefully worked out summary of experimental observation. While such summaries of observation are important for the progress of science, people still didn't know '''why''' this was true. Nevertheless, the development of Carnot's theory used that observation to explain why heat engines have limited efficiency.
Making progress on the theory required the development of the concept of entropy, and the development of statistical mechanics. To see what entropy is about, consider its thermodynamical definition as a differential. Entropy is generally symbolized with a capital S, and heat energy with a capital Q. While defining entropy in terms of its derivative rather than an actual absolute definition may seem to leave something to be desired (it leaves a "constant of integration" unspecified), that generally doesn't matter. This standard definition is used:
::<math>dS = dQ/T</math>
Why is this useful? It captures the fact that heat flows downhill. Suppose there is a hot cup of coffee in a cooler room. Heat will flow from the coffee to the room. By conservation of energy, that is, the first law of thermodynamics, the amount of heat energy flowing out of the coffee is equal to the heat energy flowing into the room.
::<math>dQ_{coffee} = -50\qquad\qquad\qquad\qquad dQ_{room} = 50</math>
So
::<math>dQ_{coffee} + dQ_{room} = 0</math>
(These would actually be instantaneous time derivatives.) Energy is conserved. But now consider the equation for entropy. It the coffee is at 310 Kelvins and the room at 290 Kelvins:
::<math>dS_{coffee} = -50/310 = -0.1613\qquad\qquad\qquad\qquad dS_{room} = 50/290 = 0.1724</math>
Because of the temperature difference, the entropy of both combined went up by 0.0111. The fact that heat flows downhill may be captured by saying that
:::Entropy always increases, or stays the same. It does not decrease.
This is still just a nicely formulated statement of observations. To see why this is the correct definition of entropy, and why this law is correct, statistical mechanics must be developed. This was done by Maxwell, Boltzmann, Clausius, and others during the 19<sup>th</sup> century.
For a continuation of this, see the [[Second Law of Thermodynamics]] article.
==[[The Third Law of Thermodynamics]]==
==[[The Third Law of Thermodynamics]]==