Answer
(a) The maximum possible efficiency of the power plant can be found using the Carnot efficiency formula:
η_carnot = 1 - T_L / T_H
where T_L is the temperature of the low-temperature reservoir (30°C + 273.15 = 303.15 K) and T_H is the highest temperature of the steam (280°C + 273.15 = 553.15 K).
η_carnot = 1 - 303.15 / 553.15 = 0.449 = 44.9%
The actual efficiency of the power plant is 29%, so it is lower than the maximum possible efficiency.
(b) The rate of waste-heat discharge to the river can be found using the formula:
Q_waste = Q_in - Q_out
where Q_in is the rate of energy input to the power plant (880 MW), and Q_out is the rate of energy output as electric power (880 MW * 0.29 = 255.2 MW).
Q_waste = 880 MW - 255.2 MW = 624.8 MW
So the rate of waste-heat discharge to the river is 624.8 MW.
(c) The number of houses that could be heated with the waste heat can be found by dividing the waste heat by the heating power required per house:
number of houses = Q_waste / P_heat
where P_heat is the heating power required per house (23 kW).
number of houses = 624.8 MW / 23 kW = 27130 houses
Therefore, the waste heat from the power plant could heat 27130 houses, each requiring 23 kW of heating power.
Work Step by Step
(a) The maximum possible efficiency of the power plant can be found using the Carnot efficiency formula:
η_carnot = 1 - T_L / T_H
where T_L is the temperature of the low-temperature reservoir (30°C + 273.15 = 303.15 K) and T_H is the highest temperature of the steam (280°C + 273.15 = 553.15 K).
η_carnot = 1 - 303.15 / 553.15 = 0.449 = 44.9%
The actual efficiency of the power plant is 29%, so it is lower than the maximum possible efficiency.
(b) The rate of waste-heat discharge to the river can be found using the formula:
Q_waste = Q_in - Q_out
where Q_in is the rate of energy input to the power plant (880 MW), and Q_out is the rate of energy output as electric power (880 MW * 0.29 = 255.2 MW).
Q_waste = 880 MW - 255.2 MW = 624.8 MW
So the rate of waste-heat discharge to the river is 624.8 MW.
(c) The number of houses that could be heated with the waste heat can be found by dividing the waste heat by the heating power required per house:
number of houses = Q_waste / P_heat
where P_heat is the heating power required per house (23 kW).
number of houses = 624.8 MW / 23 kW = 27130 houses
Therefore, the waste heat from the power plant could heat 27130 houses, each requiring 23 kW of heating power.
