Calculating a Power Plant's Energy Extraction & Efficiency

[gregbellows]

Hi, I am stuck on the question, I don't require the solution, just how to get started.

A power plant's electrical output is 750MW. Cooling water at 15oC flows through the plant at 2.8x10^4 litres/sec and its temperature by 8.5oC. Assuming the plants only energy loss is to the cooling water and that the cooling water is effectively the low temperature reservoir, determine:

1. the rate of energy extraction from the fuel
2. the plant's efficiency.

Cheers
Greg

 

[Clausius2]

. Cooling water at 15oC flows through the plant at 2.8x10^4 litres/sec and its temperature by 8.5oC.

What do you mean?. IF you're meaning $$\Delta T=8.5ºC$$ is the increasing of temperature of that water, then:

Power extracted of the fuel: $$W=W_{electric}+W_{losses}$$

The losses to the environment can be calculated:

$$W_{losses}=\rho Q c\Delta T$$

as a function of the volumetric flux Q, density and heat capacity.

Go ahead!.

 

[wais]

To get started, you will need to understand the basic principles of energy and thermodynamics. First, let's define some terms:

1. Electrical output: This is the amount of energy that the power plant produces in the form of electricity, measured in megawatts (MW).

2. Cooling water: This is the water used to cool the power plant's machinery and equipment. It is measured in liters per second (L/s).

3. Temperature change: This refers to the change in temperature of the cooling water as it passes through the power plant. In this case, the temperature increases by 8.5oC.

4. Energy loss: This is the amount of energy that is lost during the process of generating electricity. In this case, the only energy loss is to the cooling water.

Now, to calculate the rate of energy extraction from the fuel, we need to use the formula:

Power = Energy/Time

Since we know the electrical output of the power plant (750MW), we can rearrange the formula to solve for energy:

Energy = Power x Time

We also know the time, which is the rate of flow of the cooling water (2.8x10^4 L/s). So, we can plug in these values to get the rate of energy extraction from the fuel:

Energy = 750MW x (2.8x10^4 L/s)

Energy = 2.1x10^7 MW/L

Next, to calculate the plant's efficiency, we need to use the formula:

Efficiency = (Useful energy output / Energy input) x 100%

In this case, the useful energy output is the electrical output (750MW) and the energy input is the rate of energy extraction from the fuel (2.1x10^7 MW/L). So, we can plug in these values to get the plant's efficiency:

Efficiency = (750MW / 2.1x10^7 MW/L) x 100%

Efficiency = 3.57%

Therefore, the power plant's efficiency is 3.57%. I hope this helps you get started on solving the problem. Remember to always double check your units and use the correct formulas. Good luck!