Final answer:
The mass of coal required to power a 100-watt incandescent bulb over 8000 hours, compared to a 25-watt fluorescent bulb, is approximately 90 kilograms. This calculation takes into account the difference in energy consumption between the two bulbs and the average energy content of coal.
Step-by-step explanation:
The student asked how much coal would be needed to generate the extra electricity required for a 100-watt incandescent bulb, which has the same illumination as a 25-watt fluorescent bulb, over the 8000 hour lifespan of the fluorescent bulb. To calculate this, we first determine the additional energy consumption of the incandescent bulb compared to the fluorescent bulb. Over the 8000 hours, the incandescent bulb would use 8000 hours × 100 watts = 800,000 watt-hours (or 800 kWh), while the fluorescent bulb would use 8000 hours × 25 watts = 200,000 watt-hours (or 200 kWh). The difference in energy consumption is 800 kWh - 200 kWh = 600 kWh.
Assuming the average energy content of coal is about 24 MJ/kg, and 1 kWh = 3.6 MJ, the mass of coal can be calculated using: mass = energy / (energy content per mass). First, we convert 600 kWh to MJ: 600 kWh × 3.6 MJ/kWh = 2160 MJ. Then, we calculate the mass of coal: mass = 2160 MJ / 24 MJ/kg = 90 kg. So, approximately 90 kilograms of coal would be needed to power the incandescent bulb for 8000 hours compared to the fluorescent bulb.