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Number of collisions/sec for a gas atom

  • 16-05-2012 10:47pm
    #1
    Registered Users, Registered Users 2 Posts: 434 ✭✭


    Consider a single ideal gas atom bouncing between two opposite faces of a cubic container, with sides of length l.
    Using m for the mass of the gas atom and Vx (V sub x) for the velocity component, give an expression for the number of collisions per second the atom makes with one of the faces.


    Number of collisions per second with one of the faces = (1/2)(l^2)(Vx)n
    Where n is the number of gas atoms per unit volume.

    Should n be in the solution?

    If the number of atoms per unit volume, n, increases then according to the solution so do the number of collisions with one of the faces. Would that be correct?

    The higher the number of gas atoms per unit volume, the more collisions there are per second with one of the faces?

    Thank you


Comments

  • Registered Users, Registered Users 2 Posts: 147 ✭✭citrus burst


    Smythe wrote: »
    Number of collisions per second with one of the faces = (1/2)(l^2)(Vx)n
    Where n is the number of gas atoms per unit volume.

    Should n be in the solution?

    It should be, but since there is only one atom in question, n=1, so the best answer would be; here is a general solution (1/2)(l^2)(Vx)n, here is the answer with only one atom (1/2)(l^2)(Vx). Assuming the formula you give is right.
    Smythe wrote: »
    If the number of atoms per unit volume, n, increases then according to the solution so do the number of collisions with one of the faces. Would that be correct?

    Yup, as n gets bigger so do the number of collisions. The same with the velocity.
    Smythe wrote: »
    The higher the number of gas atoms per unit volume, the more collisions there are per second with one of the faces?

    Yeah same as above, more atoms equal more collisions equal higher temp etc

    Here is a link that may help you visualize what is happening, you can play around with it. http://phet.colorado.edu/en/simulation/gas-properties

    The website is pretty good for visualizing and simulating stuff


  • Registered Users, Registered Users 2 Posts: 434 ✭✭Smythe


    Thanks citrus burst, and for the link.
    Smythe wrote: »

    If the number of atoms per unit volume, n, increases then according to the solution so do the number of collisions with one of the faces. Would that be correct?

    The higher the number of gas atoms per unit volume, the more collisions there are per second with one of the faces?



    Yup, as n gets bigger so do the number of collisions.

    What I has been wondering was as n increases and therefore the total number of collisions increases, would this instead decrease the number of collisions with one of the faces? As an increase in n means it no longer has a free and easy path to bounce back and forth between the faces.


  • Registered Users, Registered Users 2 Posts: 147 ✭✭citrus burst


    Smythe wrote: »
    Thanks citrus burst, and for the link.




    What I has been wondering was as n increases and therefore the total number of collisions increases, would this instead decrease the number of collisions with one of the faces? As an increase in n means it no longer has a free and easy path to bounce back and forth between the faces.

    That's a pretty good question. You are correct that the total number of collisions increases. Unless its assumed that there is some drift or force pushing the particles in one direction this won't happen. Think of it this way, the mean free path of the particles does decrease as n increases. However when "counting" the number of collisions per second, it doesn't matter what particle hits the wall. It could be the same few over and over again, they are trapped between the wall and the particles in the middle of the box.

    If we increase the number of particles, more will be "trapped" between the middle and the wall on both sides, hence more collisions. This is a measure of pressure. PV=NkT more particles equals more pressure if the volume remains constant and pressure is essentially a measure of the number of particles hitting the walls of a container.


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