Question

B.Sc 18 seme
1. Derive the kinetic gas equation, PV = 1/3 mnu​

Answer 1

Answer:

Let us consider a gas molecule moving in the x-direction towards face A. The molecule hits the wall with a velocity Vx and rebounds back with the same velocity Vx, and will experience a change of momentum which is equal to Δp=−2mVx.

For a total of N number of gas molecules in the container, all such change in momentum is given by

Δp=−2NmVx

The force is given by the equation

F=Δpt

Therefore,

F=−2NmVxt

Gas molecules will hit the wall A and will travel back across the box, collide with the opposite face and hit face A again after a time t which is given by the equation

t=2lVx

Substituting the value of t in the force equation, we get the force on the molecules as

F=−2NmVx2lVx

Fmolecules=−2NmVx2lVx=−NmV2xl

Therefore, the force exerted on the wall is Fwall=NmV2xl.

Now, the pressure P is given by the equation

P=ForceonthewallArea=NmV2xll2=NmV2xl3

Hence, PV=NmV2x (1)

Since Vx, Vy and VZ are independent speed in three directions and if we consider the gas molecules in bulk, then

V2x=V2y=V2z

Hence,

V2=3V2x

Substituting the above condition in eq (1), we get

PV=NmV23

Therefore,

PV=13mNV2

Explanation:

hope it helps u