The velocity of particle is $(v_x, v_y, v_z)$. As shown, the side of the cube is of length $L$. Find the time taken for the particle to go from one wall to the opposite wall.

Question

ganeshie8 · Answer

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ganeshie8 · Answer

basically we need to find the time taken by the particle to go from the left wall to the right wall

ganeshie8 · Answer

ignore gravity

parthkohli · Answer

this is a great question and is a foundational one for the kinetic theory of gases

ganeshie8 · Answer

yes! also i think we assume that the collisions with walls are elastic

parthkohli · Answer

yeah, precisely. I think you know the answer to this already. not sure what you asked this for.

ganeshie8 · Answer

I have just started kinetic theory of gases, still not sure what the textbook is saying..

parthkohli · Answer

Consider the projection in the x-axis.$$T = \frac{distance}{speed} = \frac{L}{v_x}$$

ganeshie8 · Answer

aren't you assuming that the particle hits each wall with an angle 90 ?

ganeshie8 · Answer

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ganeshie8 · Answer

it can take any random route in the cube right ?

parthkohli · Answer

sorry, I was away.

ganeshie8 · Answer

formula is just $L/v_x$ right ?

ganeshie8 · Answer

assuming ofcourse $v_x \lt\lt c$

parthkohli · Answer

going from one wall to other will not change $v_x$ along the way

ganeshie8 · Answer

why

parthkohli · Answer

conservation of momentum. even if there is a collision with another wall (maybe  in the y-z plane or whatever) the momentum will be conserved along the x-direction as there are no forces acting on the ball in that direction|dw:1450171605831:dw|