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With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process. There is a fourth version of the second law of thermodynamics stated in terms of entropy :

The total entropy of a system either increases or remains constant in any process; it never decreases.

For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease.

Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant. Thus we are led to make a connection between entropy and the availability of energy to do work.

Entropy and the unavailability of energy to do work

What does a change in entropy mean, and why should we be interested in it? One reason is that entropy is directly related to the fact that not all heat transfer can be converted into work. When entropy increases, a certain amount of energy becomes permanently unavailable to do work. The energy is not lost, but its character is changed, so that some of it can never be converted to doing work—that is, to an organized force acting through a distance.

Order to disorder

Entropy is related not only to the unavailability of energy to do work—it is also a measure of disorder. This notion was initially postulated by Ludwig Boltzmann in the 1800s. For example, melting a block of ice means taking a highly structured and orderly system of water molecules and converting it into a disorderly liquid in which molecules have no fixed positions. (See [link] .) There is a large increase in entropy in the process, as seen in the following example.

Entropy associated with disorder

Find the increase in entropy of 1.00 kg of ice originally at 0º C size 12{0°C} {} that is melted to form water at 0º C size 12{0°C} {} .

Strategy

As before, the change in entropy can be calculated from the definition of Δ S size 12{ΔS} {} once we find the energy Q size 12{Q} {} needed to melt the ice.

Solution

The change in entropy is defined as:

ΔS = Q T . size 12{ΔS= { {Q} over {T} } } {}

Here Q size 12{Q} {} is the heat transfer necessary to melt 1.00 kg of ice and is given by

Q = mL f , size 12{Q= ital "mL" rSub { size 8{f} } } {}

where m size 12{m} {} is the mass and L f size 12{L rSub { size 8{f} } } {} is the latent heat of fusion. L f = 334 kJ/kg size 12{L rSub { size 8{f} } ="334"" kJ/kg"} {} for water, so that

Q = ( 1.00 kg ) ( 334 kJ/kg ) = 3 . 34 × 10 5 J. size 12{Q= \( 1 "." "00"" kg" \) \( 3 "." "34"" kJ/kg" \) =3 "." "34" times "10" rSup { size 8{5} } " J"} {}

Now the change in entropy is positive, since heat transfer occurs into the ice to cause the phase change; thus,

Δ S = Q T = 3 . 34 × 10 5 J T . size 12{ΔS= { {Q} over {T} } = { {3 "." "34" times "10" rSup { size 8{5} } " J"} over {T} } } {}

T size 12{T} {} is the melting temperature of ice. That is, T = C=273 K size 12{T=0°"C=273 K"} {} . So the change in entropy is

Δ S = 3 . 34 × 10 5 J 273 K = 1.22 × 10 3 J/K. alignl { stack { size 12{DS= { {3 "." "34"´"10" rSup { size 8{5} } " J"} over {"273 K"} } } {} #" "=1 "." "22"´"10" rSup { size 8{3} } " J/K" "." {} } } {}

Discussion

This is a significant increase in entropy accompanying an increase in disorder.

The diagram has two images. The first image shows molecules of ice. They are represented as tiny spheres joined to form a floral pattern. The system is shown as ordered. The second image shows what happens when ice melts. The change in entropy delta S is marked between the two images shown by an arrow pointing from first image toward the second image with change in entropy delta S shown greater than zero. The second image represents water shown as tiny spheres moving in a random state. The system is marked as disordered.
When ice melts, it becomes more disordered and less structured. The systematic arrangement of molecules in a crystal structure is replaced by a more random and less orderly movement of molecules without fixed locations or orientations. Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder.

In another easily imagined example, suppose we mix equal masses of water originally at two different temperatures, say 20.0º C size 12{"20" "." 0°C} {} and 40.0º C size 12{"40" "." 0°C} {} . The result is water at an intermediate temperature of 30.0º C size 12{"30" "." 0°C} {} . Three outcomes have resulted: entropy has increased, some energy has become unavailable to do work, and the system has become less orderly. Let us think about each of these results.

Practice Key Terms 3

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Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
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