##
**Conservation of linear
momentum**

According to principle of conservation
of linear momentum in case of perfectly elastic collision both the linear
momentum and kenetic energy of system conserved

imp---

if mass of balls are same than after
the collision it exchanges the velocity

Now let us suppose that the ball is
moving toward a wall

P(initial)= (m*v)*i , (i
denote the motion in only x direction)

P(final)= -(m*v)*i ,

So change in momentum of ball

=p(f) – p(i) ,

=(-2mv)*i

Now let suppose there are ‘n’ no of molecules in the container having
possible velocity

V1=(Vx1)i +(Vy1)j +(Vz1)k

V2=(Vx2)i +(Vy2)j +(Vz2)k

.

.

.

.

Vn=(Vxn)i +(Vyn)j +(Vzn)k

Pressure on the wall due to x-component
of velocity

For ball

change in momentum of ball

=p(f) – p(i) ,

=(-2mv)*i

For wall

change in momentum of ball

=p(f) – p(i) ,

=(2mv)*i

2l/v sec = time taken in 1 collision

I sec =v/2l collision

F= p*frequency

=2mv*v/2l

=mV2/l

F(x)= mv2/l(x1) + mv2/l(x2) +
mv2/l(x3)…………..mv2/l(xn)

As

Pressure =force/area

=and area=L*L

Pressure in x direction= mV2/L +mv2/L +
mv2/L+……………mv2/L

1 + 2
+ 3 +…………….
N

Same as pressure in Y direction

= mV2/L +mv2/L + mv2/L+……………mv2/L

1 + 2
+ 3 +…………….
N

And
Z-direction

= mV2/L +mv2/L + mv2/L+……………mv2/L

1 + 2
+ 3 +…………….
N

Now according to pascal law the
pressure on any surface of container is always
same means by all component

So

Px = Py = Pz = P

Adding all the pressure

P + P +P =m(V2 + V2 + V2……….. V2)/L3

1 2 3 n

3P = m(V2 + V2 + V2……….. V2)/L3

1 2
3 n

P= m(V2 + V2 + V2……….. V2)/3*L3

1 2
3 ............. n

L3=V(volume of container)

P = = m(V2 + V2 + V2……….. V2)/3*V

1 2
3 n

**This is nothing but maxwell’s theory of
kenetic gases**