Question

A steam power plant receives heat from a furnace at a rate of \(280 \mathrm{GJ} / \mathrm{h}\). Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about \(8 \mathrm{GJ} / \mathrm{h}\). If the waste heat is transferred to the cooling water at a rate of \(145 \mathrm{GJ} / \mathrm{h}\), determine (a) net power output and (b) the thermal efficiency of this power plant.

Short answer

Answer: The net power output of the power plant is approximately 35.28 MW, and the thermal efficiency of the power plant is approximately 46.69%.

Step-by-step solution

Calculate the Total Heat Input

In order to compute the net power output and the thermal efficiency of the power plant, it is necessary to first calculate the total heat input into the system. Considering the given data, we have a heat power input of 280 GJ/h from the furnace and heat losses of 8 GJ/h. So the total heat input can be computed by subtracting the heat losses from the heat input from the furnace: Total Heat Input = Heat Input from the Furnace - Heat Losses Total Heat Input = 280 GJ/h - 8 GJ/h Total Heat Input = 272 GJ/h

Calculate the Net Power Output

The net power output of the plant can be computed by subtracting the waste heat transferred to the cooling water from the total heat input into the system: Net Power Output = Total Heat Input - Waste Heat Net Power Output = 272 GJ/h - 145 GJ/h Net Power Output = 127 GJ/h

Convert Net Power Output to Watts

To make the net power output more suitable for further calculations, let's convert it to watts. Remember that 1 GJ is equal to 10^9 joules and 1 hour is equal to 3600 seconds: Net Power Output = 127 GJ/h * (10^9 J/GJ) * (1 h/3600 s) Net Power Output = 127 * (10^9 / 3600) W Net Power Output ≈ 35.28 * 10^6 W or 35.28 MW

Calculate the Thermal Efficiency

Now that we have the net power output, we can calculate the thermal efficiency of the plant. The thermal efficiency is defined as the ratio of the net output to the total input: Thermal Efficiency = (Net Power Output) / (Total Heat Input) Since we already have Net Power Output in watts, let's convert Total Heat Input to watts as well: Total Heat Input = 272 GJ/h * (10^9 J/GJ) * (1 h/3600 s) Total Heat Input ≈ 75.56 * 10^6 W or 75.56 MW Now we can find the thermal efficiency: Thermal Efficiency = (35.28 * 10^6 W) / (75.56 * 10^6 W) Thermal Efficiency ≈ 0.4669 or 46.69% So, the results are: (a) The net power output of the power plant is approximately 35.28 MW. (b) The thermal efficiency of the power plant is approximately 46.69%.

Key concepts

Understanding Heat Transfer in a Steam Power Plant

Heat transfer in a steam power plant is a critical concept that involves moving thermal energy from one point to another. In the context of the problem, we focus on the process where a furnace provides thermal energy, a portion of which is lost due to various reasons, such as heat escaping through the steam pipes. What remains after accounting for these losses is then translated into work or transferred to cooling water.

The rate of heat provided by the furnace is equivalent to 280 GJ/h, but not all of this heat is used for power generation. The plant also experiences heat losses to the ambient environment, in this case, at 8 GJ/h. Understanding these numbers is crucial to assess the efficient performance of a power plant and to determine just how much of the heat input is actually put to good use.

Key Points of Heat Transfer:

• Heat transfer is essential for converting thermal energy from a furnace into mechanical energy or electricity.
• Real-life systems like steam power plants are not perfectly insulated and experience heat losses.
• It's important to account for these losses to accurately calculate the net heat that contributes to power production.

Calculating Net Power Output of a Steam Power Plant

Calculating the net power output of a steam power plant allows engineers and operators to evaluate the plant's performance and efficiency. Following the exercise, the net power output is the amount of power that the plant can actually deliver for usage after subtracting the waste heat removed by the cooling water from the total heat input.

In our exercise, we started with a total heat input, subtracted heat losses to the surrounding environment, and then subtracted the waste heat handed off to the cooling water, yielding a result of 127 GJ/h. Then, converting this figure to a more standard unit of power measurement, watts, gives a clearer understanding of how much electrical power the plant is producing, which is 35.28 MW in this case.

Converting Units is Crucial:

• Understanding and converting between different units of power, such as gigajoules per hour to watts, is essential for consistent and accurate calculations.
• The net power output is a practical figure that reflects the real capacity of the power plant to produce electricity.

Efficiency in Energy Conversion

Energy conversion efficiency is a measure of how well a power plant converts the heat it receives into usable power. It's a critical indicator of how economically and environmentally sustainable the plant is. In our steam power plant, the thermal efficiency is found by dividing the net power output by the total heat input.

The total heat input was adjusted to 272 GJ/h after considering the heat losses, and the net power output was 35.28 MW, or 35.28 * 10^6 W. By performing the division (and converting the total heat input into watts), we determined the efficiency to be approximately 46.69%. This means that just under half of the heat input is effectively turned into electricity, with the rest being unavoidably lost to different forms of waste.

Significance of High Efficiency:

• A higher thermal efficiency indicates more cost-effective and less environmentally impactful operation.
• Efficiency calculations help guide improvements in plant design and operation.
• Understanding efficiency helps in comparing different power generation technologies.