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F 2 A N m v 2 6 V

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

P N m v 2 3 V

or, rearranged for comparison to Boyle's Law ,

P V N m v 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, P V , is a constant, in agreement with Boyle's Law . Furthermore, the product P V 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:

P V 2 3 N 1 2 m v 2

The last quantity in parenthesis can be recognized as the kinetic energy of an individual gas particle, and N 1 2 m v 2 must be the total kinetic energy ( KE ) of the gas. Therefore

P V 2 3 KE

Now we insert the Ideal Gas Law for P V to find that

KE 3 2 n R T

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.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, General chemistry ii. OpenStax CNX. Mar 25, 2005 Download for free at http://cnx.org/content/col10262/1.2
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