what is a pressure ? how is pressure related to the surface area on which it acts
Answers
Pressure is a stress. It is a scalar given by the magnitude of the force per unit area. In a gas, it is the force per unit area exerted by the change of momentum of the molecules impinging on the surface. We know from Newton's second law that a net resultant force will cause a change of momentum in a body, and that the rate of change of momentum is equal to the applied force. It is a vector relationship, so that even if the magnitude of the momentum is unchanged, a change in the direction of motion requires a resultant force. The impact of a gas molecule on a solid surface is an elastic impact so that its momentum magnitude and energy are conserved. However, because its direction of motion changes on impact, a resultant force must have been exerted by the solid surface on the gas molecule. Conversely, an equal but opposite force was exerted by the gas molecule on the solid surface. If we consider a very small area of the surface of the solid, so that over a short time interval \Delta t very few molecules collide with the solid over this area, then the force exerted by the gas molecules will vary sharply with time. When we consider a sufficiently large area, so that the number of collisions on the surface during the interval \Delta t is large, then the average force that acts on the solid surface by the molecules is constant. It is this force, acting on the surface of the solid, that we call the force due to pressure.
In practice, the area need only be larger than about 10 times (mean free path)^2, so that pressure is a continuum property, by which we mean to say that for areas of engineering interest, which are almost always much larger than areas measured in terms of the mean free path, the pressure does not have any measurable statistical fluctuations caused by molecular motions. We can make a distinction between microscopic properties and the macroscopic properties of a fluid, where the microscopic properties relate to the behavior on a molecular scale (that is, scales comparable to the mean free path), and the macroscopic properties pertain to the behavior on an engineering scale (that is, scales much larger than the mean free path).