# 0.22 Entropy and the second law of thermodynamics  (Page 5/9)

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We therefore need a new function S(W), so that, when we combine the two glasses of water, S total = S 1 + S 1 . Since S total = S(W total ), S 1 =S(W 1 ), and W total = W 1 × W 1 , then our new function S must satisfy the equation

S(W 1 × W 1 ) = S(W 1 ) + S(W 1 )

The only function S which will satisfy this equation is the logarithm function, which has the property that ln(x × y) = ln(x) + ln(y). We conclude that an appropriate state function that measures the number of microstates in a particular macrostate is

S = k ln W

## Observation 2: absolute entropies

It is possible, though exceedingly difficult, to calculate the entropy of any system under any conditions of interest from the equation S = k ln W. It is also possible, using more advanced theoretical thermodynamics, to experimentally determine S by measuring heat capacities and enthalpies of phase transitions. Values of S determined experimentally, often referred to as "absolute" entropies, have been tabulated for many materials at many temperatures. A few examples are given in Table 1 measured at pressure of 1 atm. (The superscript º on S indicates standard pressure. It turns out that, for gases, the entropy depends significantly on the pressure.) Our goal is to analyze these data in the context of Equation (1).

There are several interesting trends observed in Table 1. First, if we compare the entropy of the gaseous form of a substance to either its liquid or solid form at the same temperature, we find that the gas always has a substantially greater entropy. This makes sense from Equation (1): the molecules in the gas phase occupy a very much larger volume. There are many more possible locations for each gas molecule and thus many more arrangements of the molecules in the gas. This means that W should be larger for a gas, and therefore the entropy of a gas is greater than that of the corresponding liquid or solid.

Second, we can see in the table that the entropy of a liquid is always greater than that of the corresponding solid. This is understandable from our kinetic molecular view of liquids and solids. Although the molecules in the liquid occupy a comparable volume to that of the molecules in the solid, each molecule in the liquid is free to move throughout this entire volume. The molecules in the solid are relatively fixed in location. Therefore, the number of arrangements of molecules in the liquid is significantly greater than that in the solid, so the liquid has greater entropy by Equation (1).

Absolute entropies of specific substances
T (ºC ) Sº(J/mol·ºC )
H 2 O (g) 25 188.8
H 2 O (l) 25 69.9
H 2 O (l) 0 63.3
H 2 O (s) 0 41.3
NH 3 (g) 25 192.4
HN 3 (l) 25 140.6
HN 3 (g) 25 239.0
O 2 (g) 25 205.1
O 2 (g) 50 207.4
O 2 (g) 100 211.7
CO (g) 25 197.7
CO (g) 50 200.0
CO 2 (g) 24 213.7
CO 2 (g) 50 216.9
Br 2 (l) 25 152.2
Br 2 (g) 25 245.5
I 2 (s) 25 116.1
I 2 (g) 25 260.7
CaF 2 (s) 25 68.9
CaCl 2 (s) 25 104.6
CaBr 2 (s) 25 130
C 8 H 18 (l) 25 361.1

Third, the data show that the entropy of a substance increases with increasing temperature. We have previously found that the temperature of a substance is a measure of the average kinetic energy of the molecules in the substance. In a solid or liquid, then, increasing the temperature increases the total kinetic energy available to the molecules. The greater the energy, the more ways there are to distribute this energy amongst the molecules. Although we have previously only referred to the range of positions for a molecule as affecting W, the range of energies available for each molecule similarly affects W. As a result, as we increase the total energy of a substance, we increase W and thus the entropy.

what is the stm
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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for teaching engĺish at school how nano technology help us
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NANO
how can I make nanorobot?
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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