Particles Moving and Kinetic Energy

Statement I accurately describes a fundamental property of matter. All matter is composed of tiny particles, such as atoms or molecules, which are in constant, random motion. This continuous movement is the source of their kinetic energy. Think of it like tiny dancers constantly moving around – their movement gives them energy. Even in solids, where particles are tightly packed, they vibrate around their fixed positions, possessing vibrational kinetic energy. In liquids and gases, this motion is more significant, with particles moving freely and colliding with each other.

The kinetic energy of a single particle is given by the formula:

$ KE = \frac{1}{2}mv^2 $

Where:

• KE is the kinetic energy
• m is the mass of the particle
• v is the velocity (speed) of the particle

Since the particles are always moving (v is greater than 0), they inherently possess kinetic energy. Thus, Statement I is true.

Temperature Effect on Kinetic Energy

Statement II correctly explains the relationship between temperature and the motion of particles. Temperature is essentially a measure of the average kinetic energy of the particles in a substance. When you increase the temperature of a substance, you are adding energy to its particles. This added energy makes the particles move faster and/or vibrate more intensely. As their speed (v) increases, their kinetic energy (proportional to $v^2$) also increases significantly.

For example:

• If you heat water, the water molecules move faster and collide more forcefully.
• In a gas, increasing the temperature makes the gas particles zoom around much faster, leading to increased pressure if the volume is constant.

Therefore, an increase in temperature directly corresponds to an increase in the average kinetic energy of the particles. Statement II is true.

Overall Statement Validity

Based on the scientific principles of the kinetic theory of matter:

• Statement I is true because particles of matter are always in motion and possess kinetic energy.
• Statement II is true because temperature is a direct measure of the average kinetic energy of these particles, meaning higher temperatures lead to higher kinetic energy.

Since both statements are accurate, the correct option is the one stating that both statements are true.