Equipartiton Of Energy
Equipartition of Energy Concepts for JEE and CBSE board exams:
1. Key Points:

Equal Kinetic Energy: In a system of particles in thermal equilibrium, the average kinetic energy of each particle is equal, regardless of the particle’s mass or type.

Total Energy Conservation: The total energy of the system remains constant. Energy can be transferred between particles, but the overall energy remains the same.
2. Relationships derived from Equipartition Theorem:

Pressure and Temperature: The pressure exerted by a gas is directly proportional to its temperature. Higher temperature leads to increased molecular kinetic energy and more frequent collisions, resulting in greater pressure.

Specific Heat Capacity and Temperature: The specific heat capacity of a solid is directly proportional to its temperature. As temperature increases, more energy is required to raise the temperature of the solid by the same amount.

Root Mean Square Velocity and Temperature: The root mean square (RMS) velocity of molecules in a gas is proportional to the square root of its absolute temperature. Higher temperature corresponds to faster molecular motion and thus higher RMS velocity.
*3. Applicability:
 Thermal Equilibrium: The equipartition theorem is only valid for systems in thermal equilibrium, where there is no net transfer of energy between parts of the system.
*4. Explaining Phenomena:

Thermal Expansion: The equipartition theorem helps explain thermal expansion observed in solids and liquids. As temperature increases, the average kinetic energy of particles increases, leading to greater separation between particles and expansion.

Speed of Sound’s Temperature Dependence: The temperature dependence of the speed of sound can be understood through the equipartition theorem. Higher temperatures correspond to faster molecular motion, resulting in faster propagation of sound waves.