Seawater power plant efficiency

In summary, the problem involves a power plant that generates electricity from the difference in sea temperature. The highest efficiency it can have is 7%, based on the Carnot efficiency formula. To release 210 W of power, the plant must receive at least 3 kW from the hot sea water and release at least 2.8 kW to the cold sea water. The plant works on a Carnot cycle, assuming no other information is given.
  • #1
raymanmusic
31
1
1. Problem statement
A power plant generates electricity from the difference in sea temperature. At the surface of the sea the temperature is 27°C. At the bottom of the sea the temperature is 6°C.

a) What is the highest efficiency that this plant can have?
b) If the power plant generates 210 W of power, how much heat per time must be released by the hot sea water? How much heat per time is released into the cold sea water?


2. Equations
The Carnot efficiency: efficiency = 1-(Tc/Th)
P[supplied] = P[output]/efficiency
P[wasted] = P[supplied] – P[output]

3. Attempt at a solution
The idea here is that the power plant uses heat from the hot sea water to run a heat engine. The heat engine turns the heat into mechanical work to generate electricity. The heat engine is not efficient enough, so some heat energy is wasted. This wasted heat energy is used to heat the cold sea water.

In a) I used The Carnot efficiency: efficiency = 1-(Tc/Th)

Tc = temperature in kelvin of cold reservoir = 273.15+6
Th = temperature in kelvin of hot reservoir = 273.15+27

Efficiency = 0.0699 = 7%

In b) to find heat per time released by the hot sea water I used:

P[supplied] = P[output]/efficiency

P[output] = 210 W
Efficiency = 1-(Tc/Th) = 0.0699

P[supplied] = 3043.478 W = 3 KW

To find heat per time released into the the cold sea water I used:

P[wasted] = P[supplied] – P[output]

P[wasted] = 3043.478 W – 210 W = 2833.478 W = 2.8 KW
 
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  • #2
raymanmusic said:
P[supplied] = 3043.478 W = 3 KW
I think that you typed in a number incorrectly on your calculator, as that number is about 1% off.

Otherwise, did you have a question?
 
  • #3
Yes I meant 0.0699. I used 0.069. I'm not sure if my solution is correct, does something seem wrong in my solution? Can I use carnot efficiency equation in this case. I only know the temperatures of the reservoirs, so I'm guessing I have to use the Carnot efficiency formula.
 
  • #4
raymanmusic said:
Yes I meant 0.0699. I used 0.069. I'm not sure if my solution is correct, does something seem wrong in my solution? Can I use carnot efficiency equation in this case. I only know the temperatures of the reservoirs, so I'm guessing I have to use the Carnot efficiency formula.

Everything looks fine. Since you are not given more information, you must assume that the plant works on a Carnot cycle, otherwise you would be inventing numbers! You can also formulate the answer to say that the plant must receive at least 3.0 kW from the hot water and release at least 2.8 kW to the cold water, as these are the minimum values based on an ideal heat engine.
 
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  • #5


4. Response
Based on the given information, the highest efficiency that this power plant can have is 7%. This is calculated using the Carnot efficiency formula, which takes into account the temperature difference between the hot and cold reservoirs. In order to generate 210 W of power, the plant would need to release 3 kW of heat from the hot sea water. This means that 2.8 kW of heat is wasted in the process and is released into the cold sea water. This highlights the importance of improving the efficiency of the heat engine in order to reduce wasted heat energy and increase the overall efficiency of the power plant. Further research and development in this area could potentially lead to more efficient and sustainable ways of harnessing energy from the ocean.
 

What is a seawater power plant?

A seawater power plant is a facility that uses the energy from ocean waves to generate electricity. It typically consists of a large device called a wave energy converter, which captures the kinetic energy from the waves and converts it into electricity.

How efficient is a seawater power plant?

The efficiency of a seawater power plant can vary depending on a number of factors, such as the design of the wave energy converter, the location of the plant, and the size of the waves. On average, a seawater power plant can have an efficiency of around 50%, which is comparable to other renewable energy sources such as wind and solar.

What are the advantages of using a seawater power plant?

One advantage of a seawater power plant is that it is a clean and renewable source of energy. It does not produce greenhouse gas emissions or pollute the environment like fossil fuel power plants. Additionally, seawater is a abundant resource, making it a reliable source of energy for coastal communities.

What are the limitations of seawater power plants?

One limitation of seawater power plants is their dependence on weather conditions. If the waves are too small or too large, the plant may not be able to generate enough electricity. Additionally, the technology for wave energy conversion is still developing, so there may be challenges in terms of efficiency and cost.

Can seawater power plants be used in all locations?

No, seawater power plants are most effective in coastal areas with consistent wave patterns. They may not be suitable for inland locations or areas with calm waters. The location of the plant is an important factor in determining its efficiency and feasibility.

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