Variables of State: Pressure

Einstein, Newton, and Pascall were playing a game of hide-and-seek. Einstein counted while Pascall ran to hid. Newton drew a square on the ground and stood in it. Einstein ran from behind the tree discovoring Newton. "I've found you Newton!" Newton replied, "No, you have 1 Newton per square meter. You've found Pascall."

Generally, pressure measures the force per unit area that acts on a surface. For a gas, this force comes from the gas molecules that rebound off the surface as it travels in random directions. The gas molecules approach the walls of the container of the gas with certain velocity and undergo a collision with imparts a change in momentum of the molecule. Change in momentum means a force has acted on the molecule and by Newton's third law, a force acts on the container of the walls, resulting in pressure.

Pressure is the force over area. But it is a scalar, and not a vector. This does not seem to make sense because force is a vector.

This is actually because Force can written as the integral of pressure with respect to the are vector where this physically means summing up the force on each point.