here is the mass of the particle and is the velocity. As we can see the higher temperature causes a higher velocity.
On the other hand the pressure is caused by the momentum transfer from the gas components to the wall. This means if more or higher velocity particles impinge on the wall the pressure increases (see fig. ). Therefore the relation that an increase in the gas temperature causes an increased pressure is clear. The higher temperature leads to higher average velocities and hereby more particles (with higher velocities) can reach the wall in a given time so that the momentum transfer is increased and the pressure rises.
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