Name: path dependence in gas work
Uploaded: 2023-04-30T12:31:19.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Path Between Thermodynamics States

ضع في اعتبارك أسطوانة ذات غاز مثالي من الحجم Vo عند ضغط po مزودة بمكبس عديم الاحتكاك متصل بكتلة. يظل المكبس ثابتا بينما يكون الضغط في حالة توازن.
إذا انخفضت الكتلة بمقدار النصف ، فإن الضغط الخارجي على المكبس ينخفض بشكل متناسب. يدفع الضغط الداخلي العالي للغاز المكبس إلى الأمام حتى يتم الوصول إلى توازن جديد.
يزداد حجم الغاز. يصل النظام إلى حالة ديناميكية حرارية جديدة من خلال أداء العمل.
لنفترض أن نفس الحالة النهائية تتحقق عن طريق تقليل الكتلة على مرحلتين. في البداية ، ينخفض الضغط إلى 0.75po ، ويتم تمثيل العمل المنجز بالمنطقة الواقعة أسفل المنحنى الثاني.
بتقليل الكتلة أكثر في المرحلة الثانية ، فإن الشغل الذي يقوم به الغاز يساوي المساحة الموجودة أسفل المنحنى الثالث. إذن، فإن إجمالي الشغل الذي يقوم به الغاز في العملية الثانية هو مجموع المساحات الواقعة تحت المنحنيين.
وبالتالي ، فإن العمل الذي يقوم به الغاز يختلف باختلاف العمليات ، وبالتالي فهو وظيفة تعتمد على المسار.

<ol>
 <li>يونغ ، دكتوراه في الطب ، فريدمان ، ر. الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون. 628 (2012).</li>
 <li>OpenStax. جامعة الفيزياء المجلد 2. الصفحة 110 [نسخة الويب]. تم الاسترجاع من <a href = "https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy.">https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy.</a>.</li>
</ol>

المسار بين حالات الديناميكا الحرارية

<div style="direction:rtl">فكر في العمليتين الديناميكيتين الحراريتين اللتين تشتملان على غاز مثالي يتم تمثيلهما بواسطة المسارين AC وABC في الشكل 1: <img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;">في العملية الأولى للمسار A إلى C، يتم الاحتفاظ بالغاز عند درجة حرارة ثابتة T. ويخضع للتوسيع من المجلد V1 إلى V2. يتم التعبير عن الشغل الذي يبذله الغاز المثالي بالصيغة <img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;"> بالتعويض عن الضغط كـ nRT/V من معادلة الغاز المثالي ودمج المصطلحات، يتم الحصول على الشغل الذي يبذله الغاز المثالي عند درجة حرارة ثابتة كـ <img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;"> في العملية الثانية، للمسار A إلى B، يتم أولاً توسيع الغاز المثالي من الحجم V1 إلى V2 عند ضغط ثابت p1 عن طريق تطبيق الحرارة. يتم بعد ذلك تبريد الغاز بحجم ثابت V2 على طول المسار B إلى C، بحيث ينخفض ضغطه إلى ص2. بالنسبة للمسار A إلى B، يتم العمل تحت ضغط ثابت، لذلك <img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;"> بالنسبة للمسار B إلى C، نظرًا لأن الحجم يظل ثابتًا، فلا يتم بذل شغل بواسطة الغاز أو على الغاز بواسطة المناطق المحيطة. وبالتالي، فإن الشغل الإجمالي الذي يبذله الغاز في هذه العملية هو نفس الشغل المبذول للمسار أ إلى B. في كلتا العمليتين، يتمدد الغاز من الحجم V1 إلى الحجم V2، بحيث يكون حجمه يتغير الضغط من p1 إلى p2. ومع ذلك، فإن العمل المنجز في كلتا العمليتين مختلف. وهذا يثبت أن العمل الذي يقوم به النظام يعتمد على المسار.</div>

ضع في اعتبارك العمليتين الديناميكيتين الحرارية اللتين تتضمنان غاز مثاليا يمثلهما المساران AC و ABC في الشكل 1:

في العملية الأولى للمسار A إلى ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

The First Law of Thermodynamics

القانون الأول للديناميكا الحرارية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

path dependence in gas work

Work done by an ideal gas can depend on the path it takes between two thermodynamic states. The transcript compares two routes from state A to state C for the same gas. In both cases, the gas expands from volume V1 to volume V2, but the work is not the same.

Along path AC, the gas stays at constant temperature T. It expands from V1 to V2. The work done by the gas is found from the pressure-volume relation for an ideal gas. After substituting pressure as nRT/V and integrating, the work for this isothermal process is obtained.

Along path ABC, the gas follows two steps. First, it expands from V1 to V2 at constant pressure p1 by applying heat. Then it is cooled at constant volume V2, and its pressure drops to p2. During the constant-pressure step AB, work is done by the gas. During the constant-volume step BC, no work is done because the volume does not change.

The total work for path ABC is therefore the same as the work done during AB. Even though both paths connect the same start and end states and the pressure changes from p1 to p2, the work values are different. This shows that work done by a system is path-dependent.

Path Dependence in Gas Work

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,...

work done during volume change

Gas Work in a Piston Cylinder

Gas work in a piston cylinder describes how pressure and volume change are related in thermodynamics. In mechanics, work happens when a force moves an object. In thermodynamics, work done on a system can be estimated when the system changes volume during a process. A gas can be trapped in a cylinder with a movable piston at one end. When the gas expands from volume V1 to volume V2, it pushes on the piston and moves it by a small distance dr. If the pressure on the piston face is p and the...

path between thermodynamics states

Work done by an ideal gas can depend on the path it takes between two thermodynamic states. The transcript compares two routes from state A to state C for the same gas. In both cases, the gas expands from volume V1 to volume V2, but the work is not the same. Along path AC, the gas stays at constant temperature T. It expands from V1 to V2. The work done by the gas is found from the pressure-volume relation for an ideal gas. After substituting pressure as nRT/V and integrating, the work for this...

heat and free expansion

Two Gas Paths to the Same Volume

Heat added to a thermodynamic system can lead to the same final state through different paths. The path matters because work and heat depend not only on the initial and final states, but also on the steps in between. In this topic, an ideal gas is used to show two different ways to reach the same volume. In the first case, the gas is in a cylinder with a piston and is heated at a constant temperature. As the gas molecules absorb energy, the gas expands slowly in a controlled isothermal process.

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...

first law of thermodynamics

Heat, Work, and Internal Energy

Heat, work, and internal energy are linked by the first law of thermodynamics. This law is a generalized form of energy conservation. It explains how energy changes when heat is added to or removed from a system, and when the system does work or has work done on it. The change in internal energy equals the heat transferred into the system minus the work done by the system. Added heat increases internal energy. For that reason, heat is taken as positive when it enters the system and negative...

first law of thermodynamics: problem-solving

first-law-of-thermodynamics-problem-solving

First Law of Thermodynamics: Solving Problems

The first law of thermodynamics links internal energy, heat, and work. It states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system. This is a general form of energy conservation, and it can be used for any thermodynamic process. To solve a first-law problem, start by identifying the thermodynamic system. Then list the initial and final states of the process. Next, identify the known and unknown quantities. It is...

cyclic processes and isolated systems

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...

isothermal processes

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...

isochoric and isobaric processes

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...

heat capacities of an ideal gas i

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...

heat capacities of an ideal gas iii

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...

adiabatic processes for an ideal gas

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

pressure-and-volume-in-an-adiabatic-process

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

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...

thermodynamic potentials

Energy Forms in Thermodynamics

Thermodynamic potentials are energy-based state functions used to analyze a thermodynamic system. They help describe how a system changes under different conditions. The four main thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These potentials can be written using two of the variables pressure, volume, temperature, and entropy. In each case, the rate of change of the potential with respect to the other two variables gives useful...

maxwell's thermodynamic relations

Using Maxwell's Relations in Thermodynamics

Maxwell's thermodynamic relations help solve problems in thermodynamics. They connect partial differentials for quantities that are hard to measure in the lab with quantities that are easier to measure. This makes them useful for working with temperature, pressure, volume, and entropy. These relations come from thermodynamic potentials and the symmetry of second derivatives. Thermodynamic potentials are exact differentials, so the order of second differentiation does not change the result.

joule-thomson effect

Gas Cooling and Heating in Throttling

Gas cooling and heating in throttling is explained by the Joule-Thomson effect, also called the Joule-Kelvin effect. It describes how a fluid changes temperature when it passes through a valve or porous plug in a thermally insulated system. This type of flow is called a throttling process. In the experiment, a high-pressure gas is forced through a throttle valve or porous plug into a lower-pressure region. The gas expands as it moves into the larger volume. Work is done on the gas as it is...

key terms and concepts

Compare two ideal-gas paths between the same states and see why an isothermal route and a constant-pressure-plus-volume route give different work values.

Path Dependence in Gas Work | 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.

Florida Department of Education

SC.912.P.10

SC.912.P.10.2

Power and Energy

Energy is the total work required to drive the current through the circuit.
A rise in voltage results in more work done, passing more current, resulting ...

Energy and Work

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

First Law of Thermodynamics

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 ...

conservation-of-energy-approach-to-system-analysis

Conservation of Energy Approach to System Analysis

Source: Ricardo Mejia-Alvarez and Hussam Hikmat Jabbar, Department of Mechanical Engineering, Michigan State University, East Lansing, MI
The purpose of ...

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 ...

Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. 

Clarification statement: Emphasis is on explaining the meaning of mathematical expressions used in the model. 

Assessment Boundary: Assessment is limited to basic algebraic expressions or computations; to systems of two or three components; and to thermal energy, kinetic energy, and/or the energies in gravitational, magnetic, or electric fields.

HS-PS3-1

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 ...

Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Energy Stored in Capacitors

A parallel plate capacitor connected to a battery develops a potential difference across its plates.
By integrating the equation relating voltage and ...

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 ...

Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects). 

Clarification statement: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electrically-charged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations.

HS-PS3-2

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 ...

Electric Generator: Alternator

Electric generators induce an emf by rotating a coil in a magnetic field. A simple alternator is an AC generator that creates electrical energy that ...

Dye-sensitized Solar Cells

Source: Tamara M. Powers, Department of Chemistry, Texas A&#38;M University
Today&#39;s modern world requires the use of a large amount of energy. While ...

Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy. 

Clarification statement: Emphasis is on both qualitative and quantitative evaluations of devices. Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators. Examples of constraints could include use of renewable energy forms and efficiency. 

Assessment Boundary: Assessment for quantitative evaluations is limited to total output for a given input. Assessment is limited to devices constructed with materials provided to students.

HS-PS3-3

Heat Flow and Specific Heat

Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Since heat is a form of ...

Calorimetry

When objects at different temperatures are placed in contact with each other but isolated from everything else, they attain thermal equilibrium. A ...

statements-of-the-second-law-of-thermodynamics

Statements of the Second Law of Thermodynamics

The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius&#8217; statement ...

entropy-and-the-second-law-of-thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The ...

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 ...

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. ...

Internal Energy

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 ...

Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics). 

Clarification statement: Emphasis is on analyzing data from student investigations and using mathematical thinking to describe the energy changes both quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water. 

Assessment Boundary: Assessment is limited to investigations based on materials and tools provided to students.

Maxwell's Equation Of Electromagnetism

James Clerk Maxwell (1831&#x2013;1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

Magnetic Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Magnetic fields can be ...

Electric Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
An electric field is generated ...

Electric Charge in a Magnetic Field

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment duplicates J.J. Thomson's famous experiment at the end of ...

Electric Potential Energy

When an electric field accelerates a free positive charge q, it is given kinetic energy. The process is analogous to an object accelerated by a ...

Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. 

Clarification statement: Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other. 

Assessment Boundary: Assessment is limited to systems containing two objects.

HS-PS3-5

Path Dependence in Gas Work

Description

Transcript

More videos by Standards