The following explanation is from my textbook:
Consider a small region within a gas where the temperature increases in the $x$ direction. If $\Delta t$ is the average time between collisions, some atoms will move from box 1 to 2 and some from box 2 to 1 during this period.
If the total energy of atoms in box 1 is $U_1$, then the energy crossing the dotted line from the left is roughly $U_1/2$ since only half of the molecules will have positive $x$ velocities at this moment. Also, $l$ is the mean free path of the particles which is the distance they travel during $\Delta t$.
Now here's what I don't understand:
1- Why is the energy crossing the dotted line $U_1/2$?
2- Why does it say that only half of the molecules will have positive $x$ velocities at this moment?
Thank you in advance