The change in the internal energy of a system can be calculated using the first law of thermodynamics, which states that the change in internal energy (∆U) of a system is equal to the heat (Q) absorbed by the system minus the work (W) done by the system. Mathematically, it can be represented as:
∆U = Q - W
In this case, the system absorbed 300 kJ of heat (Q = 300 kJ) from the surroundings and performed 10 kJ of work (W = 10 kJ). To calculate the change in internal energy (∆U), we substitute these values into the equation:
∆U = 300 kJ - 10 kJ ∆U = 290 kJ
Therefore, the change in the internal energy of the system is 290 kJ.