Pressure of a gas increases due to increase of its temperature because at higher temperature

According to the kinetic theory of gases, the temperature of a gas is directly proportional to the average kinetic energy of its molecules [1]. When the temperature of a gas increases, the molecules move faster and attain higher kinetic energy [1]. Pressure is defined as the force exerted by these molecules per unit area of the container walls. As temperature rises, the molecules collide with the walls more frequently and with greater force due to their increased velocity. This increase in the number and intensity of collisions results in a higher macroscopic pressure. In an ideal gas model, intermolecular forces like attraction or repulsion are typically ignored, and internal energy is dominated by kinetic energy rather than potential energy. Therefore, the rise in pressure is fundamentally linked to the higher kinetic energies of the gas molecules.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 26: Tropical Cyclones > Vapour Pressure of Water And Rate of Evaporation > p. 358