Calculate the change internal energy (î´e) for a system that is giving off 45.0 kj of heat and is performing 855 j of work on the surroundings.

The change in internal energy of a system is given by (second law of thermodynamics)

where Q is the heat absorbed by the system and W is the work done on the system.

In order to correctly evaluate the internal energy change, we must be careful with the signs of Q and W:
Q positive -> Q absorbed by the system
Q negative -> Q released by the system
W positive -> W done on the system by the surroundings
W negative -> W done by the system on the surroundings

In our problem, the heat released by the system is  (with negative sign since it is released by the system), and the work done is  still with negative sign because it is performed by the system on the surrounding, so the change in internal energy is