The statement "total heat provided to a system at constant volume is used to change the internal energy of the system" can be justified based on the principles of thermodynamics.
In a system at constant volume, no work is performed by the system (since work is defined as the product of force and displacement, and there is no displacement at constant volume). Therefore, any energy transfer into or out of the system occurs solely in the form of heat.
The internal energy of a system is defined as the sum of the kinetic and potential energies of its particles. It is a measure of the microscopic energy associated with the motion and interactions of the particles within the system.
When heat is added to a system at constant volume, it increases the kinetic energy of the particles within the system. The increased kinetic energy leads to an increase in the internal energy of the system. This can be explained by the fact that the added heat energy is absorbed by the particles, causing them to move faster and collide more frequently, resulting in an overall increase in their kinetic energy.
Conversely, if heat is removed from the system at constant volume, the kinetic energy of the particles decreases, leading to a decrease in the internal energy of the system.
Therefore, in a system at constant volume, where no work is performed, the total heat provided to the system is indeed used to change the internal energy of the system.