Heat Engine

Thermodynamics Heat Engine:


The objective of this project is to explain the dynamics of a Heat Engine. We will discuss the theory, engineering details, efficiency and environmental impacts associated with the Heat Engine. The heat engine is a fundamental thermodynamic process and holds true for all types of engines. In this blog, we will detail the workings of the Heat Engine and explain the attributes of each step of the cycle.

Thermodynamic Principle

The Heat Engine is one of the important examples of work in the field of thermodynamics. It is directly in line with the thermodynamic principle and works according to thermodynamic law. We will study the thermodynamic laws and see how they are applied on the heat engine.

In thermodynamics, the Heat Engine is a system which converts thermal or chemical energy into mechanical energy which is then used to perform work.

Working and Principle of Heat Engine:

The heat engine consists of three parts,

  1. Hot Reservoir (High Temperature)
  2. Engine
  3. Cold Reservoir (Low Temperature)


The Heat Engine takes thermal energy from the hot reservoir and uses that energy to do mechanical work. Some of the heat is lost to the cold reservoir during the work process.

First Law of Thermodynamics applied to the Heat Engine:

The first law of thermodynamics is the law of energy conversation which states that “Energy can not be created, or destroyed, but can be changed from one form to another.”

The internal energy of a system is mathematically written as:

ΔU= Q – W

Here, ΔU is change in internal energy of a system, Q is heat added to the system and W is the work done by the system.

In accordance with the first law, the heat engine cannot create extra energy. It only transforms one form (thermal or chemical) of energy into another form (Mechanical) energy. We can observe the Pressure, Volume and Temperature relationship relevant to the Heat Engine by drawing the Pressure-Volume (PV) diagram of a heat engine. This allows us to understand the change of heat from one form to another, and also its conservation.


The PV diagram was developed by James Watt to analyze and improve the efficiency of engines. The above PV diagram is an accurate depiction of the Carnot cycle which establishes the limitations on the efficiency of engine, thus fulfilling the 2nd law of thermodynamics.

The Second Law of Thermodynamics applied to the Heat Engine:

The Second Law of Thermodynamics states that “the state of entropy of the entire universe, as an isolated system, will always increase over time.” The second law also states that “changes in the entropy in the universe can never be negative.”

When we study the second law in terms of the Heat Engine, it is the guiding principle which places constraints upon the direction of heat transfer, and the attainable efficiency of the heat engine.

The Second Law of Thermodynamics explains the constraints on heat engine that restrict it from getting 100% efficiency while extracting heat from the hot reservoir to perform work. Some amount of heat must be exhausted to a cold reservoir, and this is the Kelvin-Planck’s statement.

Schematic diagrams of the Kelvin statement:




Qh = W + Qc

According to second law, we cannot achieve:

Qh = W


Engineering details of the Heat Engine

A typical heat engine works on the principle that heat released in a combustion process produces work. The linear motion is mechanically converted to rotary motion and used to do work. An internal combustion engine works through the following cycle: fuel intake, compression, ignition, and expansion, and exhaust. This process is summarized below in Figure 1.

figure 1

Figure 2 below shows a PV diagram for the Otto cycle where

5-1 (Intake Stroke, piston pulls gas in)

1-2 (Compression Stroke)

2-3 (Combustion Stroke)

3-4 (Power Stroke)

4-1 (Exhaust Opens)

1-5 (Exhaust Stroke, piston pushes gas out)

Figure 2








This cycle is completed thousands of times a minute, which is the revolutions per minute (rpm) of the engine, depicted on a typical vehicle’s dashboard gauge. This cycle is most efficient through a reversible expansion process, which exploits the spontaneous tendency of heat flow from a hot reservoir to a cold reservoir. This cycle is best described by the Carnot Cycle, a simplification of an ideal reversible process, made possible by two isotherms and two adiabats. This alternating process is necessary, since two isotherms and two adiabatic cycles at different initial temperatures will never intersect each other. The area enclosed by the plotted cycle on the PV diagram is defined as the output, or work done.

Carnot Cycle:

The Carnot cycle is the ideal reversible process in which the working substance undergoes four processes. It is important to note that the Carnot cycle heat engine is a theoretical construct, and cannot be truly built.

1. Isothermal Expansion

2. Adiabatic Expansion

3. Isothermal Compression

4. Adiabatic Compression

Isothermal Expansion:

Isothermal means same temperature. In Isothermal expansion, the system takes the heat (Qh) from high temperature (Th) reservoir and does work on the surroundings. Comparing this to an internal combustion engine, at this point the gas inside the cylinder expands isothermally and exerts force on the piston. As a result of this force, the volume increases.









The change in temperature in this process is zero and also the change in internal energy is zero.
From first law we know that,

     ΔU= Q – W                  (Here work is done by the system)

For work done on the system,

ΔU= Q + W                  (Work done on the system)



For isothermal process,

ΔU = 0

So, this implies that.

ΔQ = -ΔW


ΔW= -PdV

ΔW= -nRTln(V2/V1)

Adiabatic Expansion:

In this process no heat is added or removed from the system. This system continues to expand. Since no heat is entering the system to do work, the temperature of the system falls to Tc.  and the volume expands to V3 from V2.









In this process,


So we write.



ΔU= nCp(Tl – Th)


Isothermal Compression:

In isothermal compression, the piston which expanded to volume V3 compresses to V4 under constant temperature Tc and the change in internal energy as explained above is zero for isothermal process. During isothermal compression the heat is taken out of the system












Adiabatic Compression:

In adiabatic compression the volume decreases and hence the temperature increases. As this is an adiabatic process, no heat is going in or out. The temperature rises back to Th and for the reversible process, the volume at the end of all four process goes back to its initial value V1.










Figure 2 shows a PV diagram for the ideal reversible Carnot cycle, while Figure 3 summarizes with a table the calculations to find Q, W, and ∆U for 1 mole at each step in the process.


figure 3

Screenshot (22)

figure 4

Work is done by the system in the first two steps, while work is done on the system in the last two steps. The engine can only be useful if the net work done is greater than zero, thus the work done by the system in the first two steps must be greater than the work done on the system.


Heat Engine Efficiency

It is impossible to build a heat engine that is 100% thermodynamic efficient per the Kelvin-Planck statement of the second law of thermodynamics. A Heat Engine works by turning heat into a different form of energy. It takes heat from a hot object and moves it thermodynamically to a cooler object. The highest efficiency a heat engine can generate is by transforming the greatest amount of heat into work. There are two main types of heat engines; internal combustion engines and external combustion engines. An internal combustion transforms fuel in a combustion chamber to mechanical energy. Generally, a gasoline engine only has a 33% efficiency rating. The equation for efficiency is energy out divided by theoretical energy in multiplied by 100%.

Efficiency = (Energy out/ Theoretical Energy in)   X 100%

Another form of a Heat Engine is the external combustion engine. In this type of engine, a fuel source is burned outside the engine. The most common type is a steam engine in which wood, or coal, is burned outside of the engine and heat is used to boil water creating steam which moves a reciprocating piston. A steam locomotive is an example of this type engine converting heat energy to work. [6] Power plants work on the same premise to produce electrical energy. An external combustion engine produces mechanical work by rotating a turbine that will in turn produce electrical energy. There is some heat (energy) lost in this process by condensation in the pipes and friction in the turbine. However, the power plant still uses 50% of heat generated to mechanical energy. This is considered the most efficient type of heat engine and is referenced in Figure 4.

evan's pic

Figure 5


In theory the most efficient Heat Engine would be the Carnot Engine. The idealized Carnot Heat Engine consists of isothermal processes and adiabatic processes. According to Carnot, there would be no loss of heat energy and 100% efficiency would be realized. A Carnot cycle is theoretical because it relies on complete reversibility of the processes, but all processes are subject to the laws of physics. This means that heat generated will not be fully converted into mechanical work due to disorder and randomness which can’t be removed from the chain of events. See Figure 5 for further details.


Figure 6

Environmental Impacts

A Heat Engine converts heat into mechanical energy. Depending on the physical features of different Heat Engines, the emissions of air pollutants, such as SOx, NOx, and CO2, will vary. Hydrocarbon Heat Engines will emit air pollutants such as CO2 which are air pollutants that cause major environmental problems.

A common air pollutant is NOx. NOx emissions occur from combustion and can deplete, or enhance, ozone concentrations. Certain forms of NOx can even contribute to acid rain. A common form of NOx is NO2, which detrimentally reacts in the atmosphere with ozone, and furthers the depletion of the ozone which is vital to life on Earth. The ozone is good, but the ozone we want to minimize is the tropospheric ozone layer, which is the ozone in the air that we breathe. The stratospheric ozone is what protects us, and the troposphere ozone layer protects from the suns ionizing radiation.

Another air pollutant is SOx. At high concentrations, SOx can harm trees and plants by damaging foliage and decreasing growth. SO2 emissions, and other sulfur oxides, can contribute to acid rain, which damages ecosystems. SOx can react with other compounds in the atmosphere to form fine particles that reduce visibility, i.e. creates a haze.

A very well-known air pollutant is CO2. CO2 is the primary greenhouse gas emitted through human activities, but can also be emitted through fossil fuel combustion such as burning oil, coal, and natural gas. When the ratio of emission to removal of CO2 is in balance, there are no environmental impacts. However, when the ratio is out of balance and more CO2 is being emitted than can be removed, or vice versa, climate change could result. CO2 is an important greenhouse gas, as it helps to keep our planet warm, but when there is too much CO2, it causes what is known as the greenhouse effect. Meaning more heat is trapped by the atmosphere, causing the planet’s temperature to increase.


Personal Viewpoints and Summary

In our opinion Heat Engines can be an extremely convenient, but an inefficient way to create mechanical energy, with Internal combustion engines being some of the most inefficient. The reasons we believe they are the most inefficient is because of their many moving parts which directly contribute to additional friction and heat loss. The amount of rotating masses causes inefficiency as well, pistons, crankshafts and camshafts all require energy to overcome their inertia and force the rotation. The theoretical Carnot Engine Cycle is a useful tool to understand the maximum possible efficiency of a heat engine. It serves as a good reference tool, however it is not something that can be replicated into a real application. In our opinion external combustion engines have a much better efficiency, and this is due to the decreased amount of moving parts, resulting in less energy loss through friction. External engines also do not require “explosive” fuels like internal combustion engines. Energy harnessed using a constant steady heat is more predictable, and can be used more efficiently than rapid sequential explosions. This is likely a reason why there is a gap in efficiency between internal and external combustion heat engines. We understand why internal combustion engines are used in transportation, and other machines, when high revolutions per minute (RPM) are required, but in terms of creating vast amounts of power, we find them to be poor options due to their negative impacts on the environment, and the availability of other better options.

















Figure 1 Credit: https://www.slideshare.net/darjipratik/heat-engine-overview

Figure 3 & 4: Credit: http://wikieducator.org/EntropyLesson2

Figure 5: Credit: www.bluffton.edu/homepages

Figure 6: Credit: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw.html