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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.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Concept development studies in chemistry 2013. OpenStax CNX. Oct 07, 2013 Download for free at http://legacy.cnx.org/content/col11579/1.1
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