Name: adiabatic compression in an engine cylinder
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 20 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.10

SC.912.P.10.2

Work Done in an Adiabatic Process

Рассмотрим метеозонд, наполненный газообразным гелием, у которого некоторое начальное давление и объем увеличиваются и адиабатически расширяются до конечного объема при уменьшении атмосферного давления. Какую работу выполняет газ?
Если начальная и конечная температуры известны, то для адиабатического процесса выполняемая работа получается из его внутренней энергии, выраженной в терминах изменения температуры.
Другой способ заключается в использовании условия для адиабатического процесса, от которого можно отнести начальное и конечное давление и объемы газа. Термины переставлены для упрощения.
Вспомните работу во время изменения объема и подставьте в нее полученное выражение давления.
Интегрируя это выражение с изменением объема, можно определить работу, выполняемую во время адиабатического процесса.
Если начальное давление газа в гелиевом шаре составляет 1 атм, а объем баллона изменяется от 25м3 до 100м3, то, подставляя известные величины в производное выражение, можно рассчитать работу, проделанную газом.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. С. 641, 642</li>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Получено из <a href="https://openstax.org/books/university-physics-volume-2/pages/3-6-adiabatic-processes-for-an-ideal-gas">https://openstax.org/books/university-physics-volume-2/pages/3-6-adiabatic-processes-for-an-ideal-gas</a></li>
</ol>

Работа, выполненная в адиабатическом процессе

Рассмотрим адиабатическое сжатие идеального газа в цилиндре автомобильного дизельного двигателя. Бензиновый пар впрыскивается в цилиндр автомобильного двигателя, когда поршень находится в своём разжатом положении. Температура, давление и объём получившейся газово-воздушной смеси составляют 20 ° C, 1.00 x 105 Н/м2, и 240 см3 соответственно. Затем смесь адиабатически сжимается до объёма 40 см3. Обратите внимание, что в фактической работе автомобильного двигателя сжатие не является квазистатическим, хотя мы и делаем это предположение здесь. Каковы давление и температура смеси после сжатия? Какова работа, выполненная во время сжатия?

Решение:

Для адиабатического процесса сжатия выражение для давления записывается как

<img alt="Equation1" src="/files/ftp_upload/13689/13689_Equation_1.svg" style="text-align: center; height: 34px;" />

Используя отношение удельной теплоёмкости воздуха 1.4 и подставляя известные величины в выражение (1), вычисляется давление смеси после сжатия.

<img alt="Equation2" src="/files/ftp_upload/13689/13689_Equation_2.svg" style="text-align: center; height: 34px;" />

Из уравнения идеального газа и используя полученное значение давления, также вычисляется температура смеси после сжатия.

<img alt="Equation3" src="/files/ftp_upload/13689/13689_Equation_3.svg" style="text-align: center; height: 34px;" />

<img alt="Equation4" src="/files/ftp_upload/13689/13689_Equation_4.svg" style="text-align: center; height: 34px;" />

<img alt="Equation5" src="/files/ftp_upload/13689/13689_Equation_5.svg" style="text-align: center; height: 10px;" />

Таким образом, определяются давление и температура смеси после сжатия в цилиндре автомобильного дизельного двигателя.

Если процесс сжатия изотермический, то значение давления изменяется от полученного значения. Это происходит потому, что в адиабатическом процессе сжатия при увеличении температуры давление становится больше. Таким образом, при впрыскивании топлива в цилиндр возле хода сжатия, смесь воздуха достигает более высокой температуры, что приводит к самовозгоранию топлива без необходимости свечей зажигания.

Зная начальное и конечное давление, работа, выполненная во время сжатия, может быть получена с помощью

<img alt="Equation6" src="/files/ftp_upload/13689/13689_Equation_6.svg" style="text-align: center; height: 34px;" />

Подставляя известные и полученные величины в указанное выражение, работа равна -1.63 Дж. Здесь отрицательный знак указывает, что работа выполнена поршнем над газово-воздушной смесью.

Рассмотрим адиабатическое сжатие идеального газа в цилиндре автомобильного дизельного двигателя. Пары бензина впрыскиваются в цилиндр ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

The First Law of Thermodynamics

Первый закон термодинамики

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

adiabatic compression in an engine cylinder

Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3.

The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real automobile engine compression is not quasi-static.

Using the adiabatic pressure relation and the molar heat capacity ratio for air, 1.4, the final pressure is found from the initial conditions and the volume change. The ideal gas law is then used with that pressure to calculate the final temperature of the mixture. The result shows that the compressed gas reaches a higher pressure and temperature than it had before.

If the compression were isothermal, the pressure would be different from the value found here. In an adiabatic compression, the temperature rises, so the pressure becomes greater. This helps explain why fuel injected near the compression stroke can ignite on its own in a diesel engine, without spark plugs.

The work done during compression is found from the initial and final pressure values. The calculated work is -1.63 J. The negative sign means the piston does work on the air-gas mixture during compression.

Adiabatic Compression in an Engine Cylinder

adiabatic-compression-in-an-engine-cylinder

thermodynamic systems

Open, Closed, and Isolated Systems

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How Internal Energy Changes in Gas Systems

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work done in an adiabatic process

Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3. The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real...

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See how adiabatic compression changes pressure, temperature, and work in an engine cylinder, using ideal gas relations and a diesel engine example.

Adiabatic Compression in an Engine Cylinder | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

SC.912.P.10.3

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-3.

Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

First Law of Thermodynamics

Energy Conservation

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Internal Energy

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Types of Kinetic Energy

The amount of kinetic energy of an object depends on its mass and speed. Consider two balls of different masses rolling down an inclined plane at the same ...

Kinetic Energy - I

It&#8217;s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the ...

Kinetic Energy - II

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s ...

Work-energy Theorem

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Work-Energy Theorem for Motion Along a Curve

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Conservation of Energy

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Conservation of Energy: Application

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Differentiate among the various forms of energy and recognize that they can be transformed from one form to others.

SC.912.P.10.1

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or ...

Work Done During Volume Change

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Path Between Thermodynamics States

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In the first process for path A to ...

Heat and Free Expansion

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The internal energy of a thermodynamic system is the sum of the kinetic and potential energies of all the molecules or entities in the system. The kinetic ...

A change in the internal energy of a system depends on the the net heat transfer into the system and the net work done by the system. The first law of ...

First Law Of Thermodynamics: Problem-Solving

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Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a ...

Isothermal Processes

A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to ...

Isochoric and Isobaric Processes

A thermodynamic process that occurs at constant volume is called an isochoric process. According to the first law of thermodynamics, heat supplied or ...

Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an ...

Thermodynamic Potentials

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Maxwell's Thermodynamic Relations

Maxwell&#39;s thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell&#39;s relations relates a partial ...

Joule-Thomson Effect

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Explore the Law of Conservation of Energy by differentiating among open, closed, and isolated systems and explain that the total energy in an isolated system is a conserved quantity.

Energy and Work

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

Enthalpy

Entropy

Power

The concept of work involves force and displacement; meanwhile, the work-energy theorem relates the net work done on a body to the difference in its ...

Power Expended by a Constant Force

The relationship between work done and the time taken to do it can be explained using the concept of power. For example, several sprinters in a race may ...

Compare and contrast work and power qualitatively and quantitatively.

Mechanisms of Heat Transfer I

Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature ...

Mechanisms of Heat Transfer II

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Absorption of Radiation

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Describe heat as the energy transferred by convection, conduction, and radiation, and explain the connection of heat to change in temperature or states of matter.

SC.912.P.10.4

Kinetic Theory of an Ideal Gas

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Molecular Kinetic Energy

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Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

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Relate temperature to the average molecular kinetic energy.

SC.912.P.10.5

Chemical Reactions

A balanced chemical equation provides the information of chemical formulas of the reactants and products involved in the chemical change. A ...

Dynamics of Circular Motion

An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed ...

Dynamics Of Circular Motion: Applications

Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the ...

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Create and interpret potential energy diagrams, for example: chemical reactions, orbits around a central body, motion of a pendulum.

SC.912.P.10.6

A. Energy is involved in all physical and chemical processes. It is conserved, and can be transformed from one form to another and into work. At the atomic and nuclear levels energy is not continuous but exists in discrete amounts. Energy and mass are related through Einstein's equation E=mc2.

B. The properties of atomic nuclei are responsible for energy-related phenomena such as radioactivity, fission and fusion.

C. Changes in entropy and energy that accompany chemical reactions influence reaction paths. Chemical reactions result in the release or absorption of energy.

D. The theory of electromagnetism explains that electricity and magnetism are closely related. Electric charges are the source of electric fields. Moving charges generate magnetic fields.

E. Waves are the propagation of a disturbance. They transport energy and momentum but do not transport matter.

Adiabatic Compression in an Engine Cylinder

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