(2/3) as constant factor In Kinetic theory of gases

In summary, the conversation discusses the general formula for pressure in the kinetic theory of gases and how it is derived from mathematical statistics. The formula takes into account the number of molecules, volume of the container, and average kinetic energy of the molecules. The conversation also touches on the importance of elastic collisions and momentum in understanding this concept. Overall, the conversation highlights the complexity and fascination of analyzing physical systems using simple models.
  • #1
TheColector
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0
Hi
I'm in high school but what I'm going to ask you is probably being teached in college.
General formula: p=(2/3)*(N/V)*Ek
p- pressure
N- amount of molecules
V- volume of the container
Ek - AVERAGE kinetic energy

I've been told by my physics teacher, that 2/3 constant factor in kinetic theory of gases is the result of using mathematical statistics. As there're lots of molecules moving all the time with high velocity and different directions, kinetic energy of each is different. Therefore we use AVERAGE kinetic energy of molecules. In order to calculate this average Ek we use mathematical statistics(which with I'm not acquired at all). All of this seems logical to me. Can you possibly tell me if all of this is correct ?
 
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  • #2
your expression is a version of the equation for the pressure of a gas derived from kinetic theory
P = 1/3(Nmc2)/V where N = number of molecules, m is the mass of 1 molecule and c is the average (rms) velocity of a molecule and V is the volume
this can be written 2/3 N/V(mc2/2)
or P = {2/3N/V} x(average KE of molecule)
 
  • #3
The 3 comes from the fact that we are in 3 dimensions.
You can get the flavour of it by considering a cubic box, and a molecule bouncing back and forth along one axis.
Each time it hits a wall it imparts an impulse 2mv (do you see why?)
If the length of the box is L then it hits that wall each period of time 2L/v. So the average force on that wall from that molecule is mv2/L.
Of course, the molecules are bouncing around in all directions, but it turns out that you get the right result if you just consider the three axes of the box, i.e. take it as though a third are bouncing along each axis.
 
  • #4
I see now. That's pretty clever way of thinking about it. What does the "2mv" stand for ?
 
  • #5
TheColector said:
I see now. That's pretty clever way of thinking about it. What does the "2mv" stand for ?
Mass x velocity = momentum. If it hits with velocity v, head on, and bounces back with velocity v, the net change in momentum is m(v-(-v))=2mv.
 
  • #6
TheColector said:
I see now. That's pretty clever way of thinking about it. What does the "2mv" stand for ?
2mc is the change in momentum due to an elastic collision of a molecule with the walls...rate of change of momentum = force on wall. ie number of collisions per second x 2mc = force
You have mc2 in the expression so it is 'nice' to have 2 x 1/2mc2 so that 1/2mc2 appears as average KE...this is where the 2 in the top line comes from...good stuff
 
  • #7
I totallly forgot about the fact that all the collisions are elastic. Thanks for enlightening me.
 
  • #8
You will probably see all this again if you take a physics or chemistry course in college. As you can see by the posts above, analyzing physical systems using simple models can be fascinating and successful and fun. This is the best advertising for these college courses.
 

FAQ: (2/3) as constant factor In Kinetic theory of gases

What does "(2/3) as constant factor" refer to in the Kinetic theory of gases?

The (2/3) as constant factor in the Kinetic theory of gases refers to the ratio of the average kinetic energy of gas molecules to the total energy of the gas. This value is also known as the specific heat ratio or adiabatic index.

What is the significance of the (2/3) as constant factor in the Kinetic theory of gases?

The (2/3) as constant factor is significant because it is a fundamental property of ideal gases. It helps to explain the relationship between temperature, pressure, and volume of a gas, and is used in equations such as the ideal gas law and the adiabatic process equation.

How is the (2/3) as constant factor determined experimentally?

The (2/3) as constant factor can be determined experimentally by measuring the temperature, pressure, and volume of a gas and using these values in the ideal gas law equation. The resulting value will be equal to (2/3) if the gas behaves ideally.

Can the (2/3) as constant factor vary for different gases?

Yes, the (2/3) as constant factor can vary for different gases. This value is dependent on the number of degrees of freedom of the gas molecules, which can vary based on the type of gas and its molecular structure.

How does the (2/3) as constant factor relate to the kinetic energy of gas molecules?

The (2/3) as constant factor is directly related to the average kinetic energy of gas molecules. It represents the portion of the total energy of a gas that is due to the random motion of its molecules. As the temperature of a gas increases, the kinetic energy of its molecules also increases, resulting in a higher (2/3) value.

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