Final answer:
The change in internal energy of a system that absorbs 1,200 J of heat and does 7,218 J of work on the surroundings is -6,018 J, indicating a decrease in internal energy.
Step-by-step explanation:
The change in the internal energy of a system can be found using the first law of thermodynamics, which states that the change in internal energy (∆U) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system on the surroundings. The formula is ∆U = Q - W.
In the case given, the system absorbs 1,200 J of heat and performs 7,218 J of work on the surroundings.
Using the formula: ∆U = 1,200 J - 7,218 J = -6,018 J.
Therefore, the change in internal energy of the system is -6,018 J. The negative sign indicates that the internal energy of the system decreases.