How does the temperature affect the atmospheric pressure?

Hint:Collision between the particles of gases and any surface creates pressure on the surface. Temperature is connected to thermal energy, when temperature increases thermal energy also increases and vice versa, this thermal energy is absorbed by the particles of gases which results in increased speeds of these particles.

Complete step by step answer:
The change in momentum will be greater if they collide with each other at greater speed hence resulting in more force on the walls of the container as a result air pressure will increase. If temperature is increased the thermal energy is increased and this thermal energy will increase the kinetic energy of the gas particles present in air.

Thus resulting in an increase of speed of the particle, overall increasing the pressure exerted by the gases present in air. Hence air pressure is increased. Mathematically (For the gases in a closed container)
\[PV\,\,=\,\,nRT\] Ideal gas equation.
here \[P\]=Pressure of the gas, \[V\]=Volume occupied by the gas, \[n\]=Number of moles of the gas, \[R\]=Universal gas constant and \[T\]=Temperature of the gas

In the given situation volume is constant. As the container is closed so exchange of matter is not possible so the number of moles remains constant. $R$ is a universal gas constant which itself is a constant.So, Ideal gas equation becomes \[P\,\,\propto \,\,T\].Hence mathematically also it is clear that pressure is directly proportional to temperature.

Thus, atmospheric pressure increases with increase in temperature.

Note:Atmospheric pressure also depends on Altitude, As the altitude increases air atmospheric pressure decreases. The number of molecules moving with most probable speed is maximum.