The rate of increase of internal energy of a system can be found using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

In this case, the heat being supplied to the system is 1000 W and the work being done by the system is 200 W.

Therefore, the rate at which the internal energy of the system increases is:

1000 W (heat supplied) - 200 W (work done) = 800 W

So, the correct answer is 800 W.