Kinetic Interpretation of Temperature
The kinetic interpretation of temperature is based on the idea that temperature is a measure of the average kinetic energy of the particles in a substance. In simple terms, the higher the temperature, the faster the particles are moving.

Derivation of Kinetic Energy in Terms of Temperature
The kinetic energy of a particle is given by the equation KE = 1/2 * m * v^2, where m is the mass of the particle and v is its velocity. In a gas, the average kinetic energy of the particles can be related to the temperature using the equation KE = 3/2 * k * T, where k is the Boltzmann constant and T is the temperature in Kelvin.
By equating the two equations, we can derive the relationship between kinetic energy and temperature:
1/2 * m * v^2 = 3/2 * k * T
v^2 = 3kT / m
This equation shows that the average velocity of the particles in a gas is directly proportional to the square root of the temperature. Therefore, as the temperature increases, the average kinetic energy of the particles also increases.

Explanation
- Temperature is a measure of the average kinetic energy of particles in a substance.
- The kinetic energy of a particle is related to its velocity and mass.
- In a gas, the average kinetic energy is proportional to the temperature.
- Deriving the relationship between kinetic energy and temperature shows that as temperature increases, the average velocity of particles also increases.
- This relationship helps us understand how temperature affects the motion of particles in a substance.