Thermal Efficiency Of Heat Engine: What, Formula, How To Find


This article discusses about thermal efficiency of heat engine. We shall break the topic into two parts. First we will study about heat engine, then about thermal efficiency and then finally about thermal efficiency of heat engine.

We cannot imagine our lives without a heat engine. Heat engines are a part of our lives since a long time now and they have made our lives a lot easier. In this article we shall study about heat engines in detail and discuss about their efficiency. We shall also discuss about different types of heat engines.

What is heat engine?

Heat engine is a mechanical device which uses principles of thermodynamics to convert heat energy to mechanical energy.

The heat energy comes from the working fluid which can be water or steam or any other fluid. The heat energy will get converted into mechanical energy after entering turbine. The converted mechanical energy can be used in many applications such as driving locomotives and even for generation of electricity.

What are the working parts of a heat engine?

The heat engine is an assembly of four major parts which work together to produce work output. These parts are given in the list below-

  • Boiler- The boiler will add heat to the working fluid. For steam engine, this heat converts the liquid water to steam. This steam contains high pressure and has the highest enthalpy. This steam is passed to the turbine in the next stage.
  • Turbine– Turbine is the main component in the heat engine. The work output is produced in the turbine as it converted the heat energy to mechanical energy. The pressure of the steam decreases during this process. However the phase does not change.
  • Condenser– Condenser will change the low pressure steam to low pressure liquid. Meaning, the gaseous phase turns into a liquid phase. The temperature of working fluid does not change hence we can say that the entire phase change process is an isothermal process.
  • Compressor– The compressor increases the pressure of liquid and pumps it to the boiler. This way the working fluid becomes a high pressure liquid after passing through a compressor.

Examples of heat engine cycles-

Inside a heat engine, the working fluid used can be different. Even the components can differ according to the type of application. The different types and hence the most commonly used heat engine cycles are discussed in the section given below-

  1. Gas cycles– The gas cycles have working fluid in the gaseous form. The most commonly used working fluid is steam. The phase of the working fluid does not change in gas only cycles. The different types of gas cycles are Carnot cycle, Brayton cycle, Stirling cycle etc.
  2. Liquid cycles– As the name itself suggests the liquid cycles use only liquid as their working fluid. The phase of the working fluid does not change. The examples of liquid cycles are Sterling cycle and heat regenerative engine.
  3. Electron cycles– Different places where electron cycles are used are thermogalvanic cell, thermotunnel cooling and thermionic emission.
  4. Magnetic cycles- A thermo magnetic motor uses magnetic cycle.

What is thermal efficiency?

Thermal efficiency is simply the ratio of work that is being produced to the heat that had been added to the engine.

Thermal efficiency tells us about how efficient a thermal engine is. To measure the amount of work produced from a given amount of heat input, we calculate thermal efficiency. The useful work is produced by turbine n heat engines. Mathematically, the thermal efficiency is given by-

Thermal efficiency = (Net work done/ Heat input)

thermal efficiency of heat engine
Image: Work done is always less than the heat input

Image credits : Wikipedia

What is thermal efficiency of heat engine

We have already discussed about thermal efficiency in the above section. Thermal energy of the heat engine is the ratio of two quantities.

The first quantity being the net work done by the turbine and other being the heat added through the boiler. The turbine does some work out of which some portion of the work is used to run compressor. The remaining work is called as net work produced by the turbine. The heat added by the boiler to the working fluid is termed as heat input in the system or heat engine.

Thermal efficiency of heat engine formula

We have discussed enough about the formula relating to thermal efficiency of heat engine.

The thermal efficiency of heat engine is given by the following formula-

Where eta means the thermal efficiency

Wnet is the net work produced by the turbine

Q1 is the heat added to the heat engine by the boiler

How to find efficiency of heat engine?

We have already discussed this in above sections. The efficiency or thermal efficiency of heat engine is defined as the ratio of work output to the heat input in the system. 

To find the net work produced in the engine, we subtract work done by turbine and work transferred to compressor for its operation. The remaining quantity is the net work done.

How to find net work produced?

It is not necessary that the net work produced is equal to the total work produced by the turbine. This is because some amount of work is transferred to the compressor for its operation.

The turbine is the major component in a heat engine that produces the work. Compressor is work absorbing device that runs after absorbing some work that is produced from the turbine. The difference between the total work produced by the turbine and the work transferred to the compressor is called as the net work done in the system or net work produced in the system.

Mathematically,

Work done = Work done by turbine – Work absorbed by compressor

Working principle of heat engine

Heat engines work on a simple principle of taking heat from a heat reservoir called as heat source, producing some work out of it and send the remaining heat to another heat reservoir called as heat sink.

The energy which is transferred in the heat engine follows the law of conservation. No extra heat is created or destroyed in this process. The heat engine will not be able to convert all of the heat to work. Some amount is always lost to the sink. Here comes the factor of efficiency that is how much work an engine can produce with a given amount of heat input.

Second law of thermodynamics for heat engine

There are some laws of thermodynamics that every heat engine follows. The second law of thermodynamics for a heat engine is given below-

Second law of thermodynamics- It is impossible for a heat engine to extract heat from a heat source and convert it entirely into work. Some amount of heat has to be transferred to the heat sink.

What is Clausius Inequality?

Clausius inequality states that for a thermodynamic cycle exchanging heat with external reservoirs and undergoing a thermodynamic cycle, the line integral of (Q/Tsurr) is less than or equal to zero.

Mathematically, we can write Clausius inequality as-

where,

del Q is the infinitesimal amount of heat absorbed by the system

Tsurr is the temperature of the surroundings

Abhishek

Hi ....I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.

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