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

Stellen Sie sich einen mit Heliumgas gefüllten Wetterballon vor, der einen gewissen Anfangsdruck und ein Volumen aufweist, das adiabatisch ansteigt und sich unter abnehmendem Atmosphärendruck zu einem endgültigen Volumen ausdehnt. Welche Arbeit leistet das Gas?
Wenn die Anfangs- und Endtemperatur bekannt sind, dann wird für einen adiabatischen Prozess die geleistete Arbeit aus seiner inneren Energie gewonnen, ausgedrückt in Form von Temperaturänderung.
Eine andere Möglichkeit besteht darin, die Bedingung für den adiabatischen Prozess zu verwenden, aus der der Anfangs- und Enddruck und das Volumen des Gases in Beziehung gesetzt werden können. Die Begriffe sind zur Vereinfachung neu angeordnet.
Rufen Sie die Arbeit während der Volumenänderung auf und ersetzen Sie sie durch den erhaltenen Druckausdruck.
Durch die Integration dieser Expression mit der Volumenänderung kann die während eines adiabatischen Prozesses geleistete Arbeit bestimmt werden.
Wenn der anfängliche Gasdruck im Heliumballon 1 atm beträgt und sich das Volumen des Ballons von 25 m3 auf 100 m3 ändert, kann durch Einsetzen der bekannten Größen im abgeleiteten Ausdruck die vom Gas geleistete Arbeit berechnet werden.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson. Seiten 641, 642</li>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion]. Abgerufen von <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>

arbeit, die in einem adiabatischen prozess geleistet wird

Betrachten Sie die adiabatische Kompression eines idealen Gases im Zylinder eines Dieselmotors. Der Benzin-Dampf wird in den Zylinder des Automotormotors eingespritzt, wenn der Kolben sich in seiner ausgefahrenen Position befindet. Die Temperatur, der Druck und das Volumen der resultierenden Gas-Luft-Mischung betragen jeweils 20 °C, 1,00 x 10^5 N/m^2 und 240 cm^3. Die Mischung wird dann adiabatisch auf ein Volumen von 40 cm^3 komprimiert. Beachten Sie, dass bei dem tatsächlichen Betrieb eines Automotormotors die Kompression nicht quasi-statisch ist, obwohl wir diese Annahme hier machen. Wie hoch sind Druck und Temperatur der Mischung nach der Kompression? Welche Arbeit wird während der Kompression geleistet?

Lösung:

Für einen adiabatischen Kompressionsprozess wird der Ausdruck für den Druck wie folgt geschrieben:

<img alt="Equation1" src="/files/ftp_upload/13689/13689_Equation_1.svg" style="text-align: center; height: 34px;" />

Durch Verwendung des molaren Wärmekapazitätsverhältnisses der Luft als 1,4 und durch Einsetzen der bekannten Größen in den Ausdruck (1) wird der Druck der Mischung nach der Kompression berechnet:

<img alt="Equation2" src="/files/ftp_upload/13689/13689_Equation_2.svg" style="text-align: center; height: 34px;" />

Aus dem idealen Gasgesetz und unter Verwendung des erhaltenen Druckwerts wird auch die Temperatur der Mischung nach der Kompression berechnet:

<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;" />

Hierbei bezeichnet γ das molare Wärmekapazitätsverhältnis. Somit werden der Druck und die Temperatur der Mischung nach der Kompression im Zylinder eines Dieselmotors bestimmt.

Wenn der Kompressionsprozess isotherm ist, ändert sich der Druckwert vom ermittelten Wert. Dies liegt daran, dass bei einem adiabatischen Kompressionsprozess der Druck größer wird, wenn die Temperatur steigt. Daher erreicht die Luftmischung bei Einspritzen des Kraftstoffs in den Zylinder nahe dem Verdichtungstakt eine höhere Temperatur, was zu einer spontanen Zündung des Kraftstoffs ohne Zündkerzen führt.

Durch Kenntnis des Anfangs- und Enddrucks kann die während der Kompression erbrachte Arbeit berechnet werden:

<img alt="Equation6" src="/files/ftp_upload/13689/13689_Equation_6.svg" style="text-align: center; height: 34px;" />

Durch Einsetzen der bekannten und ermittelten Größen in den obigen Ausdruck ergibt sich eine Arbeit von -1,63 J. Hierbei gibt das negative Vorzeichen an, dass die Arbeit vom Kolben an der Gas-Luft-Mischung erbracht wird.

Arbeit, die in einem adiabatischen Prozess geleistet wird

Betrachten Sie die adiabatische Kompression eines idealen Gases im Zylinder eines Automobildieselmotors. Der Benzindampf wird in den Zylinder eines ...

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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

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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.

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SC.912.P.10.3

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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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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

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Cyclic Processes And Isolated Systems

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In the case of a ...

Isothermal Processes

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Isochoric and Isobaric Processes

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Maxwell's Thermodynamic Relations

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Compare and contrast work and power qualitatively and quantitatively.

Mechanisms of Heat Transfer I

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Mechanisms of Heat Transfer II

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SC.912.P.10.4

Kinetic Theory of an Ideal Gas

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

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many ...

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

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Potential Energy due to Gravitation

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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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