What is defined as the total kinetic and potential energies of all particles within a system?

The correct answer is the definition of internal energy, which encompasses the total kinetic and potential energies of all particles within a system. Internal energy accounts for the energy associated with the microscopic components of a system, including the energy from molecular vibrations, rotations, and potential energy arising from intermolecular forces.

This definition is particularly important in thermodynamics as it helps explain how energy is stored, transformed, and transferred within a system. For instance, when thermal energy is added to a substance, it increases the internal energy, which may result in a rise in temperature or a change of state, illustrating the interrelationship between temperature, phase changes, and internal energy.

The other concepts, like thermal energy, mechanical energy, and kinetic energy, represent different aspects of energy. Thermal energy generally refers specifically to the energy related to the temperature of a system and is part of internal energy. Mechanical energy refers to the sum of potential and kinetic energy in a system as a whole, not taking into account the energy at the microscopic level. Kinetic energy is just the energy of motion of individual particles rather than the total energy of the system.