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

考虑一个充满氦气的气象气球，在初始压强和体积下开始上升，在大气压降低的过程中绝热膨胀至最终体积。气体对外做了多少功？
如果已知初始温度和最终温度，则对于绝热过程，可通过内能（用温度变化表示）求得所做的功。
另一种方法是利用绝热过程的条件，由此可关联气体的初始和最终压强与体积。各项经过重新排列以简化表达式。
回忆体积变化过程中的功，并将得到的压力表达式代入其中。
通过将该表达式与体积变化相结合，可以确定绝热过程中所做的功。
如果氦气球的初始气体压强为 1 atm，且气球的体积从 25 m3 变为 100 m3，则通过将已知量代入推导出的表达式，可计算出气体对外所做的功。

<ol>
	<li>Young， HD 和 Freedman， RA （2012）。大学物理与现代物理。加利福尼亚州旧金山:皮尔逊。第 641， 642 页</li>
	<li>OpenStax 的。（2019）. 大学物理学第 2 卷。[Web 版本]。取自 <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>

绝热过程中所做的功

例如汽车柴油发动机气缸中理想气体的绝热压缩。 当活塞处于膨胀位置时，汽油蒸气被喷射到汽车发动机的气缸中。 所得气体-空气混合物的温度、压力和体积为 20 °C、1.00 x 105 N/m2 和 240 cm3 ，分别。 然后将混合物绝热压缩至 40 cm3 的体积。 请注意，在汽车发动机的实际运行中，压缩不是准静态的，即使我们在这里做出这样的假设。 压缩后混合物的压力和温度是多少？ 压缩过程中做了什么功？ 解决方案： 对于绝热压缩过程，压力表达式写为 <img alt="Equation1" src="/files/ftp_upload/13689/13689_Equation_1.svg" style="text-align: center; height: 34px;"> 以空气的摩尔热容比为1.4，将已知量代入式（1）中，计算出压缩后混合物的压力。 <img alt="Equation2" src="/files/ftp_upload/13689/13689_Equation_2.svg" style="text-align: center; height: 34px;"> 根据理想气体定律并使用获得的压力值，还可以计算压缩后混合物的温度。 <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;"> 由此确定了汽车柴油机气缸内混合气压缩后的压力和温度。 如果压缩过程是等温的，则压力值会与获得的值发生变化。 这是因为，在绝热压缩过程中，如果温度升高，压力就会变大。 因此，在压缩冲程附近将燃料喷射到气缸中时，空气混合物会达到更高的温度，从而导致燃料自燃，而无需火花塞。 通过了解初始压力和最终压力，可以使用以下方法获得压缩过程中所做的功 <img alt="Equation6" src="/files/ftp_upload/13689/13689_Equation_6.svg" style="text-align: center; height: 34px;"> 将已知量和求得量代入上述表达式中，所做的功等于-1.63 J。这里的负号表示活塞对空气-燃气混合物所做的功。

考虑理想气体在汽车柴油发动机气缸中的绝热压缩过程。汽油蒸气被注入气缸内的……

Education

教育

JoVE Core

Physics

物理学

Unit 1

第一单元

The First Law of Thermodynamics

热力学第一定律

KEY TERMS AND CONCEPTS

关键术语与概念

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

A thermodynamic system is the part of the world that scientists study for its heat and energy behavior. It sits inside a surrounding environment, or surroundings. The system and the surroundings can exchange heat and do work across the boundary that separates them. The immediate surroundings affect the system most strongly because they interact with it directly. A kettle of boiling tea shows how this works in everyday life. The tea and the kettle together form the system. If the lid is open,...

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Path Dependence in Gas Work

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internal energy

How Internal Energy Changes in Gas Systems

Internal energy is the energy stored inside a thermodynamic system. It is the sum of the kinetic and potential energies of the molecules or other particles in the system. Molecular kinetic energy includes translational motion, rotation, and vibration. Molecular potential energy comes from interactions between molecules. A system’s location and overall motion do not affect its internal energy. For an ideal monatomic gas, each particle is a single atom. That means there is no rotational or...

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Heat, Work, and Internal Energy

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First Law of Thermodynamics: Solving Problems

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Net Work in a Cyclic Thermodynamic Process

A cyclic thermodynamic process returns a system to its initial state. In a cycle, the change in internal energy is zero. An isolated system is different because it has zero heat exchange and zero work, so its internal energy stays constant. For a non-isolated system, the internal energy change is zero only when the process is cyclic. The first law of thermodynamics relates internal energy, heat transfer, and work. It states that the change in internal energy is the difference between the net...

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Isothermal Expansion and Heat Transfer

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained. Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression. Here, an ideal gas in an isolated cylinder expands...

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Constant Volume and Pressure in Thermodynamics

Thermodynamic processes can happen at constant volume or at constant pressure. An isochoric process is a constant-volume process. In this case, the volume does not change, so the work done by the system is zero. The first law of thermodynamics still applies, so any heat added or removed changes the internal energy of the system only. A simple example is heating 1000 g of water from 40 degrees celsius to 70 degrees celsius at constant volume. Because the process is isochoric, no work is done by...

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Ideal Gas Heat Capacity at Constant Pressure

Heat capacity describes how much heat a substance absorbs for a given change in temperature. It is also called thermal capacity, and its SI unit is J/K. Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 K, and its SI unit is J/kg·K. The video also explains molar heat capacity. This is the amount of heat added or removed to change the temperature of 1 mole of a substance by 1 K. It can be measured at constant volume or constant pressure, and it is...

heat capacities of an ideal gas ii

Ideal Gas Heat Capacity Differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case. At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at...

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Ideal Gas Heat Capacity and Degrees of Freedom

Ideal gas heat capacity depends on degrees of freedom, which are the independent ways a gas molecule can move, rotate, and vibrate. If d is the number of degrees of freedom, the molar heat capacity at constant volume can be written in terms of d. The molar heat capacity at constant pressure can also be written using the relationship between the two heat capacities. The ratio of molar heat capacity at constant pressure to molar heat capacity at constant volume is called the ratio of heat...

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Gas Temperature Changes in Adiabatic Processes

Adiabatic processes change the temperature of an ideal gas without heat transfer. In an adiabatic compression, no heat is added, but work is done on the gas. That work raises the gas temperature. In an adiabatic expansion, the gas does work and its temperature drops. A common example is the compression of a gas-air mixture inside a car engine cylinder. The compression happens so quickly that there is no time for heat to move between the mixture and its surroundings. Even so, the work done on...

pressure and volume in an adiabatic process

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Free Expansion: Pressure, Volume, and Temperature

Free expansion shows how pressure, volume, and temperature behave when a gas expands without doing work. It is an adiabatic process, but it is not the same as adiabatic expansion. In free expansion, no work is done and the internal energy does not change. In adiabatic expansion, work is done and the internal energy changes. For an adiabatic process, the pressure-volume relation comes from the adiabatic condition. That relation does not apply to free expansion, even though the expansion is...

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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Energy Forms in Thermodynamics

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Using Maxwell's Relations in Thermodynamics

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Gas Cooling and Heating in Throttling

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key terms and concepts

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

Energy can be converted from one form into another, but all of the energy present before a change occurs always exists in some form ...

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with ...

Energy

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

Types of Potential Energy

Potential energy is also known as energy at rest or stored energy. Common types of potential energy include the gravitational potential energy stored in ...

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

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared ...

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Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

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Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

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

In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when ...

Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

In the first process for path A to ...

Heat and Free Expansion

The work done by a thermodynamic system depends not only on the initial and final states but also on the intermediate states&#8212;that is, on the path. ...

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

The first law of thermodynamics states that the change in internal energy of the system is equal to the net heat transfer into the system minus the net ...

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

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four ...

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

The Joule-Thomson effect, also known as the Joule-Kelvin effect, describes the temperature change of a fluid when it is forced through a valve or porous ...

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

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the ...

conduction-convection-and-radiation-problem-solving

Conduction, Convection and Radiation: Problem Solving

There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting ...

Radiation: Applications

The average temperature of Earth is the subject of much current discussion. Earth is in radiative contact with both the Sun and dark space; it receives ...

Absorption of Radiation

The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:

where &#963; is the Stefan-Boltzmann constant, a ...

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

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist ...

Molecular Kinetic Energy

The word &#34;gas&#34;&#160;comes from the Flemish word meaning &#34;chaos,&#34; first used to describe vapors by the chemist J. B. van Helmont. Consider ...

basic-postulates-kinetic-molecular-theory-particle-size-energy

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

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For ...

kinetic-molecular-theory-gas-laws-explain-properties-gas

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws ...

kinetic-molecular-theory-molecular-velocities-temperature-kinetic

Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a ...

behavior-gas-molecules-molecular-diffusion-mean-free-path

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

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 ...

Potential Energy due to Gravitation

Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which it ...

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The Principle of Superposition and the Gravitational Field

The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a ...

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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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