Final answer:
A gas heater is more energy efficient overall than an electric water heater when the electricity comes from a coal-fired power plant due to lower direct efficiency of the electric water heater.
Step-by-step explanation:
A gas heater is more energy efficient overall than an electric water heater when the electricity comes from a coal-fired power plant due to multiple factors:
- Electric water heater has a lower direct efficiency: An electric water heater achieves 100% efficiency in converting the delivered energy into heat, but this is not the case for the overall system. The process of generating electricity at the power plant and transmitting it to the house incurs losses at each step, resulting in lower overall efficiency.
- Energy efficiency of the coal-fired power plant is low: Coal power plants typically convert only about 30-40% of the chemical energy in the coal into electricity, leading to a significant loss of energy.
- Natural gas does not need to be transported: Natural gas, which is commonly used in gas heaters, does not need to be transported over long distances like coal for power plants. This reduces energy losses associated with transportation and makes gas heaters more efficient.