Question

Derive the relation between pressure and mean kinetic energy of a gas

Answer 1

Kinetic energy is the energy possessed by an object by virtue of its motion.

K.E=1/2 mV²

Derivation:

Let us consider an object of m which is at rest lying on a table.

Let A force F acts on the object which moves the object through a distance S.

The workdone=FxS

W=FnetXS-------(1)

Let the workdone on the object causes a change in its velocity from u to V and let a be the acceleration.

From Third equation of motion:

V²-u²=2as

s=V²-u²/2a----------(2)

By Newton's Second law:

F=ma------(3)

From equation (1), (2) and (3)

W=ma*(V²-u²/2a)\=(1/2)m(V²-u²)

As we assumed object at rest, u=0

W=(1/2)mV²

we know that the kinetic energy of a body moving with certain velocity is equal to workdone on the object to acquire that velocity from rest.

∴K.E=1/2 mV²