Final answer:
Using the first law of thermodynamics, the change in internal energy (ΔU) of a system that does 511 kJ of work and loses 261 kJ of heat is calculated as ΔU = Q - W, which equals -772 kJ, indicating a decrease in internal energy.
Step-by-step explanation:
To calculate the change in internal energy (ΔU) of a system, we use the first law of thermodynamics, which is given by ΔU = Q - W, where Q is the heat added to the system, and W is the work done by the system on its surroundings. In the given situation, the system does 511 kJ of work (W) and loses 261 kJ of heat (Q) to the surroundings. Since the heat is lost, Q will be negative.
Applying the first law of thermodynamics:ΔU = Q - W = (-261 kJ) - (511 kJ) = -772 kJ.
Therefore, the change in internal energy of the system is -772 kJ, indicating that the system's internal energy has decreased by this amount.