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2.6 Examples of entropy changes

Take-home message: Spontaneous changes are aways associated with entropy increase.

Below we have various examples of entropy change during various processes. From them we can draw some general conclusions. First we see in general the entropy of anything increases when it is heated, and the entropy of a gas increases when it expands at constant temperature. A common theme (to be explored in more detail later) is that an increase in entropy is associated with an increase in disorder.

Examples of spontaneous processes are the flow of heat from a hotter to a colder body (see Ex. 1) and the free expansion of a gas (see Ex. 4). In both of these, the total entropy increases (though that of parts of the system may decrease). This is completely general: spontaneous processes are those which increase entropy.

Since heat flow from hotter to colder bodies is irreversible, reversible processes must involve heat flow between bodies of the same temperature. It follows that any entropy change of the system ${\rm d}S_{\rm sys}={}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}Q^{\rm rev}/T$ must be exactly balanced by that of the heat bath which provided the heat: ${\rm d}S_{\rm res}=-{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}Q^{\rm rev}/T$. Thus the entropy change of the universe during reversible processes is zero.

During an adiabatic process no heat flows. Thus from ${\rm d}S={}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}Q^{\rm rev}/T$ we see that the entropy change of a system during for a reversible, adiabatic process is zero. But note that both qualifiers are needed; the entropy of a non-isolated system can change during a reversible process (and the entropy change of the surroundings will compensate), and an irreversible change to an isolated system will increase the entropy (see Ex. 1&4).


Try these problems for yourself before checking the detailed answers!

next up previous contents index
Next: 2.7 The Fundamental Thermodynamic Relation Previous: 2.5 Entropy
Judith McGovern 2004-03-17