A system gives off 196 kJ of heat to the surroundings and the surroundings do 4.20 x 10³ kJ of work on the system. What is the change in internal energy of the system?

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To find the change in internal energy of the system, we can apply the First Law of Thermodynamics, which 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:

ΔU = Q - W

Given that the system gives off 196 kJ of heat to the surroundings (Q = -196 kJ) and the surroundings do 4.20 x 10³ kJ of work on the system (W = 4200 kJ), let's plug these values into the equation:

ΔU = (-196 kJ) - (4200 kJ)

Now, let's perform the calculation:

ΔU = -4416 kJ

Therefore, the change in internal energy of the system is -4416 kJ. The negative sign indicates that the internal energy of the system has decreased.