Internal Energy of the System of Particles on a 2D Sphere
Internal energy of the system of n non-interacting classical point particles constrained to move on a 2D surface such as a sphere can be understood through the following points:

1. Definition of Internal Energy
Internal energy is the total energy contained within a system, including both kinetic and potential energy of the particles. In this case, the kinetic energy of the particles is related to their motion on the sphere.

2. Energy of Non-interacting Particles
Since the particles are non-interacting, their individual energies do not depend on the positions or velocities of other particles. Each particle's energy is solely determined by its motion on the sphere.

3. Constraint of Motion on a 2D Sphere
The constraint of motion on a 2D sphere limits the possible configurations and velocities of the particles. The energy of each particle will depend on its angular momentum and position on the sphere.

4. Calculation of Internal Energy
To calculate the internal energy of the system, one would need to sum up the individual energies of all n particles. This would involve considering the kinetic energy associated with the motion on the sphere for each particle.

5. Relationship to Temperature
The internal energy of the system is related to the temperature of the system through the equipartition theorem, which states that each degree of freedom contributes 1/2 kT to the total energy, where k is the Boltzmann constant and T is the temperature.
In conclusion, the internal energy of a system of n non-interacting classical point particles moving on a 2D sphere can be understood in terms of the kinetic energy associated with their motion on the sphere. The total internal energy of the system is the sum of the energies of all individual particles, which are constrained by the motion on the sphere.