# 0.1 The kinetic molecular theory  (Page 4/7)

 Page 4 / 7

Based on our observations and deductions, we take as the postulates of our model:

• A gas consists of individual particles in constant and random motion.
• The individual particles have negligible volume.
• The individual particles do not attract or repel one another in any way.
• The pressure of the gas is due entirely to the force of the collisions of the gas particles with the walls of thecontainer.

This model is the Kinetic Molecular Theory of Gases . We now look to see where this model leads.

## Derivation of boyle's law from the kinetic molecular theory

To calculate the pressure generated by a gas of $N$ particles contained in a volume $V$ , we must calculate the force $F$ generated per area $A$ by collisions against the walls. To do so, we begin by determining the number of collisions of particles withthe walls. The number of collisions we observe depends on how long we wait. Let's measure the pressure for a period of time $\Delta (t)$ and calculate how many collisions occur in that time period. For a particle to collide with the wall within the time $\Delta (t)$ , it must start close enough to the wall to impact it in that period of time. If the particle is travelling with speed $v$ , then the particle must be within a distance $v\Delta (t)$ of the wall to hit it. Also, if we are measuring the force exerted on the area $A$ , the particle must hit that area to contribute to our pressure measurement.

For simplicity, we can view the situation pictorially here . We assume that the particles are moving perpendicularly to the walls. (This is clearly not true. However,very importantly, this assumption is only made to simplify the mathematics of our derivation. It is not necessary to make thisassumption, and the result is not affected by the assumption.) In order for a particle to hit the area $A$ marked on the wall, it must lie within the cylinder shown, which is of length $v\Delta (t)$ and cross-sectional area $A$ . The volume of this cylinder is $Av\Delta (t)$ , so the number of particles contained in the cylinder is $×((Av\Delta (t))(), \frac{N}{V})$ .

Not all of these particles collide with the wall during $\Delta (t)$ , though, since most of them are not traveling in the correct direction. There are six directions for aparticle to go, corresponding to plus or minus direction in x, y, or z. Therefore, on average, the fraction of particles moving inthe correct direction should be $\frac{1}{6}$ , assuming as we have that the motions are all random. Therefore, the numberof particles which impact the wall in time $\Delta (t)$ is $×((Av\Delta (t))(), \frac{N}{6V})$ .

The force generated by these collisions is calculated from Newton’s equation, $F=ma$ , where $a$ is the acceleration due to the collisions. Consider first a singleparticle moving directly perpendicular to a wall with velocity $v$ as in . We note that, when the particle collides with the wall, the wall does not move, so the collision must generally conservethe energy of the particle. Then the particle’s velocity after the collision must be $-v$ , since it is now travelling in the opposite direction. Thus, the change in velocity of the particle inthis one collision is $2v$ . Multiplying by the number of collisions in $\Delta (t)$ and dividing by the time $\Delta (t)$ , we find that the total acceleration (change in velocity per time) is $\frac{2ANv^{2}}{6V}$ , and the force imparted on the wall due collisions is found bymultiplying by the mass of the particles:

#### Questions & Answers

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
how did you get the value of 2000N.What calculations are needed to arrive at it
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