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

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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:

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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
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
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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