Answer
(a) The plant’s electric power output is given by the difference between the solar power delivered to the towers and the waste heat rejected to the environment:
Electric power output = Solar power input – Waste heat rejected
Electric power output = 610 MW – 233 MW = 377 MW
(b) The efficiency of the plant is given by the ratio of the electric power output to the solar power input, assuming the plant operates as a Carnot engine:
Efficiency = Electric power output / Solar power input
The solar power input is converted to heat, so we can use the formula for the efficiency of a Carnot engine in terms of the temperatures of the hot and cold reservoirs:
Efficiency = 1 – Tc / Th
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
We know that the plant rejects waste heat to the environment at 320 K, so Tc = 320 K. To find Th, we can use the fact that the heat transfer fluid is heated to a temperature considerably hotter than water and steam in nuclear and coal plants, which typically operate at temperatures around 500-600 K. Let's assume that the fluid in Ivanpah's towers is heated to a temperature of 800 K. Then, we have:
Efficiency = 1 – Tc / Th = 1 – 320 K / 800 K = 0.6
So the efficiency of the plant is 60%.
(c) The temperature of the fluid in the towers is the temperature of the hot reservoir in our Carnot cycle model. We found that a temperature of 800 K gives an efficiency of 60%, so this is our answer:
Temperature of fluid in towers = Temperature of hot reservoir = 800 K
Work Step by Step
(a) The plant’s electric power output is given by the difference between the solar power delivered to the towers and the waste heat rejected to the environment:
Electric power output = Solar power input – Waste heat rejected
Electric power output = 610 MW – 233 MW = 377 MW
(b) The efficiency of the plant is given by the ratio of the electric power output to the solar power input, assuming the plant operates as a Carnot engine:
Efficiency = Electric power output / Solar power input
The solar power input is converted to heat, so we can use the formula for the efficiency of a Carnot engine in terms of the temperatures of the hot and cold reservoirs:
Efficiency = 1 – Tc / Th
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
We know that the plant rejects waste heat to the environment at 320 K, so Tc = 320 K. To find Th, we can use the fact that the heat transfer fluid is heated to a temperature considerably hotter than water and steam in nuclear and coal plants, which typically operate at temperatures around 500-600 K. Let's assume that the fluid in Ivanpah's towers is heated to a temperature of 800 K. Then, we have:
Efficiency = 1 – Tc / Th = 1 – 320 K / 800 K = 0.6
So the efficiency of the plant is 60%.
(c) The temperature of the fluid in the towers is the temperature of the hot reservoir in our Carnot cycle model. We found that a temperature of 800 K gives an efficiency of 60%, so this is our answer:
Temperature of fluid in towers = Temperature of hot reservoir = 800 K
