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

Considere um balão meteorológico cheio de gás hélio com alguma pressão e volume iniciais subindo e se expandindo adiabaticamente para um volume final sob pressão atmosférica decrescente. Qual é o trabalho feito pelo gás?
Se as temperaturas inicial e final são conhecidas, então, para um processo adiabático, o trabalho realizado é obtido a partir de sua energia interna, expressa em termos de mudança de temperatura.
Outra maneira é usar a condição para o processo adiabático, a partir do qual as pressões e volumes iniciais e finais do gás podem ser relacionados. Os termos são reorganizados para simplificação.
Recupere o trabalho durante a mudança de volume e substitua a expressão de pressão obtida nele.
Ao integrar esta expressão com a mudança de volume, o trabalho realizado durante um processo adiabático pode ser determinado.
Se a pressão inicial do gás no balão de hélio for de 1 atm e o volume do balão mudar de 25 m3 para 100 m3, então, substituindo as quantidades conhecidas na expressão derivada, o trabalho realizado pelo gás pode ser calculado.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Física Universitária com Física Moderna. São Francisco, CA: Pearson. Pág. 641, 642</li>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão Web]. Obtido de <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>

trabalho realizado em um processo adiabático

Considere a compressão adiabática de um gás ideal no cilindro de um motor diesel de um automóvel. O vapor de gasolina é injetado no cilindro de um motor de automóvel quando o pistão está em sua posição expandida. A temperatura, pressão e volume da mistura de gasolina e ar resultante são 20 °C, 1,00 x 105 N/m2 e 240 cm3, respectivamente. Em seguida, a mistura é comprimida adiabaticamente para um volume de 40 cm3. Observe que, na operação real de um motor de automóvel, a compressão não é quasi-estática, embora estejamos fazendo essa suposição aqui. Qual é a pressão e a temperatura da mistura após a compressão? Qual é o trabalho realizado durante a compressão?

Solução:

Para um processo de compressão adiabática, a expressão para a pressão é escrita como

<img alt="Equation1" src="/files/ftp_upload/13689/13689_Equation_1.svg" style="text-align: center; height: 34px;" />

usando a razão de capacidade térmica molar do ar como 1,4 e substituindo as quantidades conhecidas na expressão (1), a pressão da mistura após a compressão é calculada.

<img alt="Equation2" src="/files/ftp_upload/13689/13689_Equation_2.svg" style="text-align: center; height: 34px;" />

A partir da lei dos gases ideais e usando o valor de pressão obtido, a temperatura da mistura após a compressão também é calculada.

<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;" />

Assim, a pressão e a temperatura da mistura após a compressão dentro do cilindro de um motor diesel de um automóvel são determinadas.

Se o processo de compressão for isotérmico, então o valor da pressão muda do valor obtido. Isso ocorre porque, em um processo de compressão adiabática, se a temperatura aumentar, a pressão se torna maior. Portanto, ao injetar o combustível no cilindro próximo à fase de compressão, a mistura de ar atinge uma temperatura mais alta, resultando em ignição espontânea do combustível sem a necessidade de velas de ignição.

Conhecendo a pressão inicial e final, o trabalho realizado durante a compressão pode ser obtido usando a fórmula:

<img alt="Equation6" src="/files/ftp_upload/13689/13689_Equation_6.svg" style="text-align: center; height: 34px;" />

Substituindo as quantidades conhecidas e as obtidas na expressão acima, o trabalho realizado é igual a -1,63 J. Aqui, o sinal negativo indica que o trabalho é realizado pelo pistão na mistura de ar e gasolina.

Trabalho Realizado em um Processo Adiabático

Considere a compressão adiabática de um gás ideal no cilindro de um motor diesel de automóvel. O vapor da gasolina é injetado no cilindro de um ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

The First Law of Thermodynamics

A Primeira Lei da Termodinâmica

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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.

Adiabatic Compression in an Engine Cylinder | JoVE K12

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SC.912.P.10.3

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-3.

Energy Basics

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First Law of Thermodynamics

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Internal Energy

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Kinetic Energy - I

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Kinetic Energy - II

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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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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 ...

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Power

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Compare and contrast work and power qualitatively and quantitatively.

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SC.912.P.10.4

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Relate temperature to the average molecular kinetic energy.

SC.912.P.10.5

Chemical Reactions

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Dynamics of Circular Motion

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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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