In a certain process, 6000 J of heat is added to a system while the system does work equivalent to 9000 J by expanding against the surrounding atmosphere. What is the change in internal energy for the system?

The absorption of heat by the system tends to raise the energy of the system. The performance of work by the system, on the other hand, tends to lower the energy of the system because performance of work requires expenditure of energy. Therefore the change in internal energy ΔU, of a system is equal to the head added to the system minus the work done by the system:

ΔU = UB – UA = q – w

Here q = 6000 j and W = 9000 j

Therefore, change in internal energy
ΔU = 6000 J – 9000J = – 3000 J

Hence, the change in internal energy for the system is equal to – 3000 J