Final answer:
When 400 J of heat is added to a system and it does 250 J of work, the internal energy of the system increases by 150 J according to the first law of thermodynamics.
Step-by-step explanation:
To determine what happens to the internal energy of a system when heat is added and work is done, we can use the first law of thermodynamics. This law is given by the formula ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
In this case, the student puts 400 J of heat into the system (Q = +400 J) and the system does 250 J of work (W = 250 J). As per the first law of thermodynamics, the change in internal energy (ΔU) would be calculated as follows:
ΔU = Q - W
ΔU = 400 J - 250 J
ΔU = 150 J
Therefore, the internal energy of the system increases by 150 J.