(Solved): Water is being heated in a closed pan on top of a range while being stirred by a paddle wheel. Dur ...

Water is being heated in a closed pan on top of a range while being stirred by a paddle wheel. During the process, \( \mathrm{Q}_{\text {in }}(\mathrm{kJ}) \) of heat is transferred to the water, and \( \mathrm{Q}_{\mathrm{our}}(\mathrm{J}) \) of heat is lost to the surrounding air. The paddle-wheel work amounts to \( \mathrm{W}_{\text {in }}(\mathrm{N} \cdot \mathrm{m}) \). Determine the final energy of the system if its initial energy is \( 10 \mathrm{~kJ} \).