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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Internal energy = heat + work
heat = -196 kJ
work = 4200 kJ
Internal energy = -196 kJ + 4200 kJ
Internal energy = -196 kJ + 4200 kJ
To find the change in internal energy of the system, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
ΔU = Q - W
In this case, 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 = -4.20 x 10³ kJ).
Plugging in these values into the equation:
ΔU = -196 kJ - (-4.20 x 10³ kJ)
= -196 kJ + 4.20 x 10³ kJ
Calculating the sum:
ΔU = 4.00 x 10³ kJ
Therefore, the change in internal energy of the system is 4.00 x 10³ kJ.