# 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.

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
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!