Kinetic theory of Gases
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| Discuss Kinetic theory of Gases KINETIC THEORY OF GASES
VAN DER WAAL’S EQUATION
As we have read earlier, the ideal gas equation is given by
PV = nRT
This equation is an example of an equation that relates the pressure, volume and the thermodynamic temperature of an amount n of a gas. This equation is thus the equation of state for a gas. Since this equation is applicable only in the case of ideal gases, this equation takes no account of the volume occupied by the gas molecules nor the intermolecular forces of the gas. In order to overcome this difficulty, J.D. van der Waals proposed a more accurate equation of state, as
|
(P + n2a/v2)( V- nb) = nRT |
Where a and b are the van der Waals constants and their value depends upon the nature of the gas. These constants are independent of the temperature and pressure of the gas.
Real gases obey this equation over wide ranges of temperature and pressure and hence it is also called the equation of state for real gases.
NOTE: Some appreciable deviations have been observed at very low temperatures and very high pressures. This can be explained by the slight variation of the constants a and b at temperatures too low and pressures too high.
KINETIC THEORY OF GASES
What is the Kinetic Theory of gases?
The Kinetic Theory is a Theory that explains the physical properties of matter in terms of the motion of its elementary particles. The kinetic theory of gases deals with the physical properties of the gases ie. Their pressure, velocity density etc. in other words it is a mathematical representation and explanation of the behaviour of gases
ASSUMPTIONS OF THE KINETIC THEORY OF GASES
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All gases are made up of a large number of small particles, called molecules. These molecules keep moving randomly in all directions.
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The intermolecular forces between the molecules are negligible and the molecules are considered like point masses. Thus, the molecules have only translational motion in the three independent axes. It is because of this negligible force that the intermolecular distance is not fixed and thus, the shape and size of the molecule is also not fixed.
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The size of the molecules is much smaller as compared to the distance between them, and thus the volume of the gas molecules is negligible as compared to the volume of the gas .
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The gravitational force of attraction is negligible on these molecules and thus they can rise against gravity owing to their kinetic energies.
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The pressure exerted by a gas is the result of the collisions of the molecule son the walls of the container.
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The collisions between the molecules and well as the collisions with the walls of the container are perfectly elastic. The time spent during a collision is very small.
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The velocity of these molecules is equally probable in all directions during their random motion, with respect to the centre of mass.
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Since each molecule in a system moves with a different kinetic velocity, all the molecules have different kinetic energies. However the average kinetic energy of the molecules can be calculated experimentally.
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The molecules obey the Newton’s Laws of motion.
NOTE: the above assumptions hold true only in the case of ideal gases. As far as the real gases are concerned these assumptions apply to a certain extent only.
THE KINETIC GAS EQUATION
Mathematically the kinetic theory can be stated as
| PV = 1/3 mnu2 |
Where
P is the pressure of the gas
V is the volume of the gas
m is the mass of a molecule
n is the number of molecules present in the given volume of gas ( not the number of moles)
u is the root mean square velocity of the molecules
from the above details it can be derived
| u = (3RT/M)1/2 = (3PV/M)1/2 =(3P/d)1/2 |
Where M is the molecular weight and d the density of the gas.
