Molecules are too small to be seen by microscope. Motion of molecules can be concluded by observations seen in experiment,such as diffusion of ink particles in water,light scattering experiments etc.

$\begin{array}{l} P=\dfrac { 1 }{ 3 } \dfrac { { mN } }{ V } v _{ rms }^{ 2 } \ \therefore p\propto mv _{ rms }^{ 2 } \ so\, \dfrac { { { P _{ 2 } } } }{ { { P _{ 1 } } } } =\dfrac { { { m _{ 2 } } } }{ { { m _{ 2 } } } } \times { \left( { \dfrac { { { v _{ 2 } } } }{ { { v _{ 1 } } } }  } \right) ^{ 2 } } \ =\dfrac { { { m _{ 1 } }/2 } }{ { { m _{ 1 } } } } { \left( { \dfrac { { 2{ v _{ 1 } } } }{ { { v _{ 1 } } } }  } \right) ^{ 2 } } \ =2 \ { P _{ 2 } }=2{ P _{ 1 } } \ =2{ P _{ 0 } } \end{array}$

$Answer:-$ B

Due to motion of molecules of ink in water, it moves around the water and slowly mixes with water.Overall a diffusion process takes place between the particles of ink and particles of water.

Since the pressure and volume of gas remains same , therefore , there will not be any change in the temperature of the gas molecules.

Since brownian motion explains the collision between particles and their scattering, it is an evidence in support of kinetic theory of gases which is based on movement of particles in force fields of other particles and collision and scattering with them.

A drop of ink when poured in water gradually moves in the entire quantity of water and mixes to make the colour blueish.This is due to the diffusion of ink particles into the water particles.

Solids have least degree of freedom. Liquids have more degree of freedom and gases have least degree of freedom.Degree of motion is proportional to the extent upto which a molecule can move freely.

Pouring boiling water into a glass is highly likely to shatter it because the hot water contacts only a few part of the glass first whereas the other parts of the glass (such as the outside of the cup) remain cooler. The glass thus does not expand as a whole, but is pulled in different directions as part of it expands and part does not. This difference produces the shattering.

Hot water mixes with cold water due to motion of water molecules and total volume attains same temperature.Overall a diffusion of particles take place between hot and cold water.

Sugar mixes in water because of motion of sugar molecules around water molecules.Overall a diffusion process is seen in it as sugar particles diffuse into water particles.

As molecules are heated, they gain kinetic energy and hence speed.We already know that kinetic energy is proportional to temperature of random moving particles.

Due to diffusion, smoke molecules leave the chimney and spreads in the atmosphere.Overall a diffusion process is seen in it as smoke particles diffuse into air particles.

As a liquid is heated, its molecules gain kinetic energy, motion of molecules is increased and the liquid expands.Overall interparticle distance increases.

In convection, heat transfer occurs because of motion of molecules of substance in upward direction.Convection, occurs due to temperature differences which affect the density, and thus relative buoyancy, of the fluid. Heavier (more dense) components will fall, while lighter (less dense) components rise, leading to bulk fluid movement.

As a solute is added to the water and mixed, its molecules are spread across the volume of water and solute is then dissolved in water.

When perfume is sprayed in corner of a room, its molecules moves around the room due to diffusion spreading the fragrance. Overall a diffusion process is seen in it as perfume particles diffuse into air particles.