Fifteen joules of heat are added to a cylinder with a piston. the system uses 7 joules of energy to raise the piston upward. by how much did the internal energy of the system increase? 2 joules 8 joules 15 joules 22 joules

The first law of thermodynamics states that:

where 
is the variation of internal energy of the system
Q is the heat absorbed by the system
L is the work done by the system on the surrounding.

In this problem, the system absorbs 15 J of heat, so Q=+15 J (with positive sign, since it is heat absorbed by the system) while the work done by the system is L=+7 J (with positive sign, since it is work done by the system), so the variation of internal energy is