If the gas particles are of diameter 'd', average speed 'v', number of particles per unit volume 'n', then the volume a particle sweeps in time 't' is?

CONCEPT:

• The gas particles are very small and spherical in shape.

The surface area of a sphere is given by:

A = 4 π r²

Where r is the radius of the sphere.

Volume (V) = Area (A) × Length (L)

EXPLANATION:

Given that:

Diameter = d

Average speed = v

Time = t

Length (or distance)  travel of the particle (L) = v t

Radius (r) = d/2

Area (A) = 4 π r2 = 4 π (d/2)2 = π d²

So volume swift (V) = Area (A) × Length (L) = π d2vt

Hence option 1 is correct.