# 0.1 The kinetic molecular theory  (Page 5/7)

 Page 5 / 7
$F=\frac{2ANmv^{2}}{6V}$

To calculate the pressure, we divide by the area $A$ , to find that

$P=\frac{Nmv^{2}}{3V}$

or, rearranged for comparison to Boyle's Law ,

$PV=\frac{Nmv^{2}}{3}$

Since we have assumed that the particles travel with constant speed $v$ , then the right side of this equation is a constant. Therefore the product of pressure times volume, $PV$ , is a constant, in agreement with Boyle's Law . Furthermore, the product $PV$ is proportional to the number of particles, also in agreement with the Law of Combining Volumes . Therefore, the model we have developed to describe an ideal gas is consistent with ourexperimental observations.

We can draw two very important conclusions from this derivation. First, the inverse relationship observedbetween pressure and volume and the independence of this relationship on the type of gas analyzed are both due to the lackof interactions between gas particles. Second, the lack of interactions is in turn due to the great distances between gasparticles, a fact which will be true provided that the density of the gas is low.

## Interpretation of temperature

The absence of temperature in the above derivation is notable. The other gas properties have all beenincorporated, yet we have derived an equation which omits temperature all together. The problem is that, as we discussed atlength above, the temperature was somewhat arbitrarily defined. In fact, it is not precisely clear what has been measured by thetemperature. We defined the temperature of a gas in terms of thevolume of mercury in a glass tube in contact with the gas. It is perhaps then no wonder that such a quantity does not show up in amechanical derivation of the gas properties.

On the other hand, the temperature does appear prominently in the Ideal Gas Law . Therefore, there must be a greater significance (and less arbitrariness) to the temperaturethan might have been expected. To discern this significance, we rewrite the last equation above in the form:

$PV=\frac{2}{3}N\frac{1}{2}mv^{2}$

The last quantity in parenthesis can be recognized as the kinetic energy of an individual gas particle, and $N\frac{1}{2}mv^{2}$ must be the total kinetic energy ( $\mathrm{KE}$ ) of the gas. Therefore

$PV=\frac{2}{3}\mathrm{KE}$

Now we insert the Ideal Gas Law for $PV$ to find that

$\mathrm{KE}=\frac{3}{2}nRT$

This is an extremely important conclusion, for it reveals the answer to the question of what property is measuredby the temperature. We see now that the temperature is a measure of the total kinetic energy of the gas. Thus, when we heat a gas,elevating its temperature, we are increasing the average kinetic energy of the gas particles, causing then to move, on average, morerapidly.

## Analysis of deviations from the ideal gas law

We are at last in a position to understand the observations above of deviations from the Ideal Gas Law . The most important assumption of our model of the behavior of an idealgas is that the gas molecules do not interact. This allowed us to calculate the force imparted on the wall of the container due to asingle particle collision without worrying about where the other particles were. In order for a gas to disobey the Ideal Gas Law , the conditions must be such that this assumption isviolated.

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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