Final answer:
The change in the system's internal energy is found using the first law of thermodynamics, which results in a change of 50 J based on the given heat and work values.
Step-by-step explanation:
To calculate the change in the system's internal energy, we apply the first law of thermodynamics. This law states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system.
In this scenario, initially 80 J (Q₁) is added to the system and the system does 20 J (W₁) of work. Later, 30 J (Q₂) is added, and the system does 40 J (W₂) of work. Therefore, the change in internal energy is calculated as
ΔU = (Q₁ - W₁) + (Q₂ - W₂)
ΔU = (80 J - 20 J) + (30 J - 40 J)
ΔU = 60 J + (-10 J)
ΔU = 50 J
Therefore, the change in internal energy of the system is 50 J.