Final answer:
The change in internal energy (δu) of water falling in a hydroelectric dam is essentially zero because the gravitational potential energy is converted into other forms, not lost as internal energy. Theoretical gravitational potential energy calculation for 1.0 kg of water falling 33 meters would indicate 330 J, but in reality, this is fully converted to kinetic and subsequently electrical energy, so the δu is zero.
Step-by-step explanation:
The change in internal energy (δu) of 1.0 kilogram of water falling 33 meters in a hydroelectric dam can be calculated using the gravitational potential energy formula, which is Potential Energy (PE) = mass (m) × gravitational acceleration (g) × height (h). In this case, the gravitational acceleration (g) is approximately 9.8 m/s², and since the water falls and its potential energy is converted into kinetic energy, which is further used to spin turbines and generate electricity, we assume no gain in internal energy, hence δu = 0, because energy is conserved and converted rather than lost or gained.
However, for theoretical purposes to calculate the potential energy before conversion, we use the given values: m = 1.0 kg, g = 9.8 m/s², and h = 33 m. The calculation would be: PE = 1.0 kg × 9.8 m/s² × 33 m = 324.9 J, which approximates to 330 J when considering significant digits.
Therefore, the correct answer for the gravitational potential energy before conversion into electrical energy is (a) 330 J, but the actual change in internal energy δu is zero because of energy conservation during the conversion process.