Answer:
The change in the internal energy of the system can be calculated using the First Law of Thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W).
ΔU = Q - W
In this case, the surroundings are gaining 3500 J of heat energy (Q = +3500 J), and 670 J of work is performed by the surroundings (W = -670 J). The negative sign for work indicates work done by the system (surroundings performing work on the system).
Plugging the values into the equation:
ΔU = 3500 J - (-670 J)
ΔU = 3500 J + 670 J
ΔU = 4170 J
Therefore, the change in the internal energy of the system is 4170 J.