1. **Problem Statement:** A closed system has an initial internal energy of 230 kJ. It rejects 80 kJ of heat and 37 kJ of work is done on the system. Find the final internal energy using the First Law of Thermodynamics. 2. **Formula and Explanation:** The First Law of Thermodynamics for a closed system is: $$\Delta U = Q - W$$ where $\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done by the system. Important: Heat rejected means $Q$ is negative, and work done on the system means work done by the system is negative. 3. **Calculations:** Given: - Initial internal energy $U_i = 230$ kJ - Heat rejected $Q = -80$ kJ - Work done on system $W_{on} = 37$ kJ, so work done by system $W = -37$ kJ Calculate change in internal energy: $$\Delta U = Q - W = (-80) - (-37) = -80 + 37 = -43 \text{ kJ}$$ Final internal energy: $$U_f = U_i + \Delta U = 230 - 43 = 187 \text{ kJ}$$ 4. **Answer:** The final internal energy of the system is **187 kJ**.