Does pressure increase as temperature increases in a gas at a constant volume?
This phenomenon is readily explained by the kinetic-molecular theory of gases.
Pressure of a gas is caused by the gas particles colliding with the walls of its container.
Simply put, because there is not a change in the volume, the temperature increase causes more collisions with the walls per unit time (as temperature increases, the average kinetic energy and thus the speed of the gas particles increases). Also because they're moving faster, the momentum with which they strike the container walls also increases. A greater number of collisions and the force of those collisions causes the pressure to increase.