Final answer:
At the same temperature, heavy and light particles have different kinetic energy distributions, with lighter particles moving faster than heavier ones to achieve the same kinetic energy. With increasing temperature, the kinetic energy distribution widens for all particles, indicating a wider range of speeds. The Maxwell-Boltzmann distribution curve helps to illustrate the variations in speed distribution between light and heavy particles.
Step-by-step explanation:
Comparing Kinetic Energy and Speed Distributions
At the same temperature, heavy and light particles have different kinetic energy and speed distributions. Kinetic energy (KE) is directly proportional to the mass of the particle and the square of its velocity (KE = ½ mv²). At a given temperature, substances have the same average kinetic energy per molecule; however, this does not mean that heavy and light particles will have the same speed. For particles to have the same kinetic energy, a lighter particle must move faster than a heavier one.
When the temperature increases, particles move faster. Absolute zero refers to the theoretical temperature at which particles have minimum internal energy and cease their motion. The motion of gas particles is random and constant, with collisions between them being perfectly elastic, meaning no net loss of kinetic energy. The relationship between the kinetic energy of gas particles and the temperature of the gas is that the average kinetic energy is proportional to the absolute temperature.
The speed distribution of molecules in a gas is often illustrated by the Maxwell-Boltzmann distribution curve, which shows that at any given temperature, light particles (having less mass) have a Broader and shifted distribution of speeds compared to heavier particles. This is due to the fact that lighter particles require higher speeds to achieve the same kinetic energy as heavier particles. Thus, if we keep the temperature constant, heavy particles move at slower speeds on average, and light particles move at higher speeds in order to have the same average kinetic energy.
Considering the metabolic rates of animals for kinetic energy, larger animals need much greater energies for movement, linking to higher metabolic rates. The kinetic energy is also reflected in molecular behavior in gases; when pressure is increased by reducing the volume at constant temperature, the average kinetic energy remains the same. However, if the temperature is increased at constant volume, the average kinetic energy increases, parallel to an increase in pressure.
In summary, the distribution of kinetic energies becomes broader and flatter as the temperature increases, signifying a wider range of possible speeds. At the same temperature, light and heavy particles have different distributions of speed, and thus, their kinetic energy distributions are different as well.