derive an expression for pressure exerted by a gas molecule on the wall of the container
Answers
Answer:
The molecules of gas are in random motion. So, they exert pressure on the walls of the container and strike with the walls of the container. Therefore, they exert thrust or force on the wall. The thrust exerted by molecules per unit area of the wall of the container is called pressure.
Answer:
Let u, v, w be the components of velocity along x, y, Z axis of container.
C1^2=u1^2+v1^2+w1^2
C2^2=u2^2+v2^2+w2^2
Cn^2=un^2+vn^2+wn^2
Again let us assume, u1 is velocity along x axis
mu1=initial momentum before striking the wall
-u1=rebounds after striking
mu1-(-mu1) =2mu1
Time taken by gas molecule bet.two successive collision is 2l/u1
Force exerted=change in momentum /time taken
=2mu1/2l/u1=mu1^2/l
Pressure exerted by this molecule along x axis is,
P1x=force/area
=mu1^2/l/l^2
=mu1^2/l^3
Similarly, pressure exerted by other molecules along x axis are
P2x=mu2^2/l^3 p3x=mu3^2/l^3........ Pnx=mun^2
Therefore, total pressure exerted by all molecules along x axis is
Px=p1x+p2x+...... +pnx
=(mu1^2+mu2^2+......+mun^2)/l^3