Problems
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Problems
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Problem II
It is known that the kinetic energy of the hard disks is only dependent on T. For a low density hard disk system, explain why thermal conductivity k is independent of the density of the hard disks ρ. (Hint, the hard disks could transfer heat by direct translating from the hot region to the cold region, or by colliding with other hard disks, which one is more efficient? Why?)
2). You may assume that a hard disk gas with l greater than or close to 10 times the hard disk diameter D is an ideal/close-to-ideal hard disk gas. Find out whether k is independent of ρ for an ideal hard disk gas using the applet, use N = 25 to 150 to model ideal or close-to-ideal situations. Explain your result and critically comment on your conclusion in part 1) (Hint: compare L and l and remember heat transfer could also occur by translation of the hot disk to the cold region)
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1). Assume heat is being transferred from a 2-D hot wall (red) to a 2-D cold wall (blue) by conduction through a gas made up of 2-D hard disks. The temperatures of the walls are fixed. The average distance traveled by a hard disk between two successful collisions l is much larger than its diameter D, i.e. the density of the hard disk gas is not too high. The distance between the two walls is L. L is much greater than l, i.e. the density of the hard disk is not too low.