The gas expands at constant pressure because the temperature increases.
According to the KMT, a temperature increase causes an increase in the average velocity of particles. This, in turn, causes an increase in the force of impact and hence on the pressure that the particles exert on average onto the internal walls of the container.
As soon as the pressure increases, the volume increases. This causes, in turn, a reduction in the average frequency of collisions, until the pressure is restored to the initial value.
The final result is that, as the temperature increases, the volume increases in the same ratio, while the pressure is kept constant.
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