Answer
The power plant extracts thermal energy at the rate of 3810 MW, of which 1250 MW is converted into electrical energy. Therefore, the remaining thermal energy is wasted.
The amount of energy required to heat one home in a winter month is 43.2 GJ. Let's first convert this to watts:
43.2 GJ = 43.2 × $10^9$ J
1 month = 30 × 24 × 60 × 60 s = 2,592,000 s (approx.)
Energy required per second = (43.2 × $10^9 $J) / 2,592,000 s ≈ 16,667 W
If 100% of the waste heat from the power plant is used for home heating, then the amount of energy available for heating is:
3810 MW - 1250 MW = 2560 MW
Let's convert this to watts:
2560 MW = 2,560,000 kW = 2,560,000,000 W
The number of homes that can be served by this amount of energy is:
Number of homes = (2,560,000,000 W) / (16,667 W/home) ≈ 153,600 homes
Therefore, 100% of the waste heat from the power plant can serve 153,600 homes.
Work Step by Step
The power plant extracts thermal energy at the rate of 3810 MW, of which 1250 MW is converted into electrical energy. Therefore, the remaining thermal energy is wasted.
The amount of energy required to heat one home in a winter month is 43.2 GJ. Let's first convert this to watts:
43.2 GJ = 43.2 × $10^9 $J
1 month = 30 × 24 × 60 × 60 s = 2,592,000 s (approx.)
Energy required per second = (43.2 ×$ 10^9 $J) / 2,592,000 s ≈ 16,667 W
If 100% of the waste heat from the power plant is used for home heating, then the amount of energy available for heating is:
3810 MW - 1250 MW = 2560 MW
Let's convert this to watts:
2560 MW = 2,560,000 kW = 2,560,000,000 W
The number of homes that can be served by this amount of energy is:
Number of homes = (2,560,000,000 W) / (16,667 W/home) ≈ 153,600 homes
Therefore, 100% of the waste heat from the power plant can serve 153,600 homes.
