# 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.

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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