Why do you think particles in warm temperature rise while the particles in cooler temperature sink?

Particles in warm temperature rise while the particles in cooler temperature sink:

Temperature is a calculation of the mean kinetic energy of a substance's atoms or molecules. Heat is the transition of energy from a material at higher to a material at lower temperature. When heat is provided, the particles in liquids and gases acquire kinetic energy, which increases vibration and start moving faster.

Thus as the particles travel farther apart, they take up more space, due to which particles in warm temperature rises, as it allows the liquid or gas to move upward. While cooler liquid or gas travel downward because no external energy is provided to them, thus on acquiring low temperature, the inter-molecular forces between particles increase which deduct spaces between them.

b.have there own function.

since there are no options posted i'll give you a few examples.

a dolphin's flipper, bird's wing, cat's leg.