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.