Question

Based on thermal efficiency, approximately two-thirds of the energy input by heat transfer in the steam generator of a power plant is ultimately rejected to cooling water flowing through the condenser. Is the heat rejected an indicator of the inefficiency of the power plant?

Short answer

The heat rejected is not an indicator of the inefficiency but a result of the second law of thermodynamics inherent in thermal power plants.

Step-by-step solution

Understanding Thermal Efficiency

Thermal efficiency is the ratio of the work output of the power plant to the heat input. It measures how effectively a power plant converts heat energy into useful work.

Calculating Energy Distribution

Given that two-thirds of the energy input is rejected to cooling water, it indicates that only one-third is converted into useful work. This can be expressed as: \[ \text{Useful Work} = \frac{1}{3} \times \text{Heat Input} \] and \[ \text{Heat Rejected} = \frac{2}{3} \times \text{Heat Input} \]

Evaluating Heat Rejected

The rejection of heat is part of the thermodynamic process. According to the second law of thermodynamics, not all the heat energy can be converted into work.

Assessing Power Plant Inefficiency

While the heat rejected might seem to be a waste, it is an inherent feature of thermal power plants. High rejection does not inherently indicate inefficiency but reflects the limitations imposed by thermodynamic laws.

Key concepts

thermodynamics

Thermodynamics is the study of energy, heat, and their interactions.
It involves understanding how energy transforms from one form to another and how it affects matter.
The main laws of thermodynamics help us analyze power plants and engines.
The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed.
The second law of thermodynamics introduces the concept of entropy and states that energy transformations are not 100% efficient.
This means that some energy is always lost as unusable heat.
These laws are crucial in determining how efficiently a power plant can convert heat energy into useful work. Understanding these principles can help us improve the efficiency of energy systems and develop new technologies.

heat transfer

Heat transfer is the process by which thermal energy moves from one object or substance to another.
This occurs through conduction, convection, and radiation.
In a power plant, heat transfer plays a key role in the energy conversion process.
The steam generator heats water to produce steam, which drives turbines to generate electricity.
Heat is transferred from the steam to the surrounding environment, usually through condensers and cooling systems.
Understanding heat transfer helps engineers design more efficient systems.
For example, improving heat exchangers can reduce energy losses and enhance overall thermal efficiency.

power plant efficiency

Power plant efficiency measures how well a power plant converts fuel into useful electrical energy.
It is expressed as a percentage and is calculated by comparing the energy input to the energy output.
High efficiency means more of the fuel's energy is converted into electricity, while lower efficiency means more energy is wasted.
There are many factors affecting power plant efficiency, including the type of fuel, the technology used, and how well the plant is maintained.
Improving efficiency involves optimizing the thermodynamic processes and minimizing energy losses.
This can result in lower operating costs and reduced environmental impact.

second law of thermodynamics

The second law of thermodynamics states that energy transformations are never completely efficient.
It introduces the concept of entropy, which measures the disorder or randomness of a system.
According to this law, in any energy conversion process, some energy is always lost as heat.
This is why no power plant can be 100% efficient.
In the context of a thermal power plant, a significant portion of the heat input is inevitably rejected to cooling water.
This heat rejection is not a sign of inefficiency but a natural consequence of the second law.
Recognizing this helps us set realistic expectations and work towards improving other aspects of power plant performance.