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Entropy
Energy change in the surroundings of a system can be used to deduce entropy changes in these surroundings and in the system itself.

In considering the thermodynamics of changes, chemical or otherwise, we must focus on the initial and the final states that are connected by a real or imagined process. We would like to know whether there is a property that lets us deduce whether a natural, spontaneous process might change in the system from one state to another.

Spontaneity and reversibility: before proceeding, we must introduce terms that are used when we deal with the tendency of a process or reaction to occur, if there is such a tendency, the process is said to be spontaneous. The rolling of a ball down an incline is a spontaneous process. Now in a rolling ball example, think of a steepness of the incline being reduced. The tendency of a ball to roll will become less. The spontaneity of the process decreases. In the limit when the ball is on a level section, the spontaneity is reduced to zero. We say that at this stage the rolling of a ball is a reversible, or balanced, process. The words are intended to suggest that a small change in the slope one way or the other will make the process spontaneously one way to the other. In contrast, spontaneous are said to be irreversible. No small change in the factors that affect the tendency of the reaction will proceed to make the opposite direction the spontaneous one.

Chemical terminology has it that spontaneous, or irreversible, are processes in which a “driving force” tends to make the process occur in a particular direction. A balanced, or irreversible, is one in which this driving force is zero. The system is at a state of equilibrium.

We now begin the development of a property, called entropy that lets us deal quantitively with the extent to which a reaction or chemical process is spontaneous or irreversible. We arrive at a property that serves our purposes by beginning with arbitrary quantities defined for the thermal and mechanical surroundings. From these quantities we develop a corresponding property of the system.

The change in the energy of the system and the change in the energy of the thermal surroundings for the vaporization of 1 mol of water molecules at 100 degree C (373 K):

(i) ∆Smech m = 0

(ii) ∆H = 40.670 J
            
H2O (I) H2O (g)

(iii) ∆ Utherm = - 40.670 J

∆Stherm = - 40.670 J/373 K
     
= - 109 JK
-1

Example: change in entropy when temperature changes: what is the difference in the entropy of a liquid after sample that contains 1 mol of water molecules at 0 and 100˚C? The measured heat capacity CP in this temperature range can be taken as equal to the 25˚C value of 75.5 Jk-1 mol-1.

Solution: think of the nearly reversible addition of energy to the water sample from the thermal surroundings. We need to imagine that these surroundings can have a variable temperature that can be just of the water sample.

The entropy change of the thermal surroundings is calculated first. We use:

∆Stherm = ∫ dUtherm/T

With, dUtherm = -CP dT

And, CP = 75.5 JK-1 mol
-1

In this way we obtain:

∆Stherm = -∫373273 (75.35 In T]373273 = -75.5 (5.922 – 5.609)

= -23.6 Jk-1 mol-1

The entropy of the thermal surroundings decreases as energy is supplied to raise the temperature of the water.

In the process that we are imaging, the energy transfer is reversible. The entropy of the universe will not change. It follows, since ∆Smech is always zero, that ∆S = -∆Stherm and,

∆S = +23.6 Jk-1 mol-1.

Liquid water at 100˚C has 23.6 Jk-1 mol-1 more of the quantity that we call entropy than 0˚C.

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