# 0.6 Equilibrium and the second law of thermodynamics  (Page 5/11)

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We therefore need a new function $S(W)$ , so that, when we combine the two glasses of water, ${S}_{\mathrm{total}}={S}_{1}+{S}_{1}$ . Since ${S}_{\mathrm{total}}=S({W}_{\mathrm{total}})$ , ${S}_{1}=S({W}_{1})$ , and ${W}_{\mathrm{total}}=×({W}_{1}, {W}_{1})$ , 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 theproperty that $\ln ×(x, y)=\ln x+\ln y$ . We conclude that an appropriate state function which measures thenumber of microstates in a particular macrostate is [link] .

## Observation 2: absolute entropies

It is possible, though exceedingly difficult, to calculate the entropy of any system under any conditions ofinterest from the equation $S=k\ln W$ . It is also possible, using more advanced theoreticalthermodynamics, to determine $S$ experimentally by measuring heat capacities and enthalpies of phase transitions. Values of $S$ determined experimentally, often referred to as "absolute" entropies, havebeen tabulated for many materials at many temperatures, and a few examples are given in [link] . We treat these values as observations and attempt to understand thesein the context of [link] .

Absolute entropies of specific substances
T (°C ) S ( $\frac{J}{\mathrm{mol}\mathrm{°C}}$ )
${H}_{2}O\left(g\right)$ 25 188.8
${H}_{2}O\left(l\right)$ 25 69.9
${H}_{2}O\left(l\right)$ 0 63.3
${H}_{2}O\left(s\right)$ 0 41.3
$N{H}_{3}\left(g\right)$ 25 192.4
$H{N}_{3}\left(l\right)$ 25 140.6
$H{N}_{3}\left(g\right)$ 25 239.0
${O}_{2}\left(g\right)$ 25 205.1
${O}_{2}\left(g\right)$ 50 207.4
${O}_{2}\left(g\right)$ 100 211.7
$CO\left(g\right)$ 25 197.7
$CO\left(g\right)$ 50 200.0
$C{O}_{2}\left(g\right)$ 24 213.7
$C{O}_{2}\left(g\right)$ 50 216.9
${\mathrm{Br}}_{2}\left(l\right)$ 25 152.2
${\mathrm{Br}}_{2}\left(g\right)$ 25 245.5
${I}_{2}\left(s\right)$ 25 116.1
${I}_{2}\left(g\right)$ 25 260.7
$\mathrm{Ca}{F}_{2}\left(s\right)$ 25 68.9
$\mathrm{Ca}{\mathrm{Cl}}_{2}\left(s\right)$ 25 104.6
$\mathrm{Ca}{\mathrm{Br}}_{2}\left(s\right)$ 25 130
${C}_{8}{H}_{18}\left(s\right)$ 25 361.1

There are several interesting generalities observed in [link] . First, in comparing the entropy of the gaseous form of a substance to eitherits liquid or solid form at the same temperature, we find that the gas always has a substantially greater entropy. This is easy tounderstand from [link] : the molecules in the gas phase occupy a very much larger volume. Thereare very many more possible locations for each gas molecule and thus very many more arrangements of the molecules in the gas. It isintuitively clear that $W$ should be larger for a gas, and therefore the entropy of a gas is greaterthan that of the corresponding liquid or solid.

Second, we observe that the entropy of a liquid is always greater than that of the corresponding solid. Thisis understandable from our kinetic molecular view of liquids and solids. Although the molecules in the liquid occupy a comparablevolume to that of the molecules in the solid, each molecule in the liquid is free to move throughout this entire volume. The moleculesin the solid are relatively fixed in location. Therefore, the number of arrangements of molecules in the liquid is significantlygreater than that in the solid, so the liquid has greater entropy by [link] .

Third, the entropy of a substance increases with increasing temperature. The temperature is, of course, ameasure of the average kinetic energy of the molecules. In a solid or liquid, then, increasing the temperature increases the totalkinetic energy available to the molecules. The greater the energy, the more ways there are to distribute this energy amongst themolecules. 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.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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 .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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