The work done on a system by external forces is equal to the change...

According to the work-energy theorem, the work done by all forces (external and internal) on a system is equal to the change in its kinetic energy:

$W_{\text{ext}} + W_{\text{int}} = \Delta K$

The internal work done can be split into work done by conservative internal forces and non-conservative internal forces:

$W_{\text{int}} = W_{\text{int, c}} + W_{\text{int, nc}}$

The work done by conservative internal forces is equal to the negative of the change in potential energy:

$W_{\text{int, c}} = -\Delta U$

The work done by non-conservative internal forces results in a change in the internal energy (such as thermal energy) of the system:

$W_{\text{int, nc}} = -\Delta U_{\text{int}}$

Substituting these into the first equation:

$W_{\text{ext}} - \Delta U - \Delta U_{\text{int}} = \Delta K$

$W_{\text{ext}} = \Delta K + \Delta U + \Delta U_{\text{int}}$

The sum of kinetic energy, potential energy, and internal energy constitutes the total energy of the system:

$W_{\text{ext}} = \Delta E_{\text{total}}$

Thus, the work done by external forces on a system is equal to the change in its total energy.