Name: isothermal expansion and heat transfer
Uploaded: 2025-08-19T15:10:28.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Louisiana Student Standards for Science

High School

Chemistry

Energy

HS-PS3-4

Isothermal Processes

일정한 온도에서 발생하는 열역학적 과정을 등온 과정이라고 합니다.
섭씨 100도의 일정한 온도에서 끓는 물을 증기로 변환하는 것이 등온 공정의 한 예입니다. 마찬가지로, 섭씨 0도에서 물이 얼음으로 바뀌는 것도 등온 과정입니다.
온도가 변하지 않기 때문에 이러한 과정에서 내부 에너지의 변화는 0입니다. 따라서 열역학 제1법칙을 사용하면 수행된 작업은 열과 같습니다.
이제 일정한 온도에서 밀폐된 가스 주사기에 들어 있는 이상 가스 시스템을 생각해 보십시오.
플런저를 제어된 방식으로 천천히 밀면 주사기 내부의 가스가 압축됩니다. 가스의 부피가 감소하면 압력이 증가하지만 온도는 일정하게 유지됩니다.
제어된 방식으로 플런저를 해제하면 일정한 온도에서 가스가 팽창합니다.
모든 등온 공정에 대한 pV 곡선은 압력이 일정한 온도에서 이상 기체의 부피에 반비례하기 때문에 쌍곡선입니다.

<ol>
	<li>Young, H. D 및 Freedman, RA (2012). 현대 물리학을 가진 대학 물리학. 샌프란시스코, 캘리포니아 : 피어슨. 635쪽.</li>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전]. pp 121 원본 주소 <a href="https://openstax.org/books/college-physics/pages/15-2-the-first-law-of-thermodynamics-and-some-simple-processes">https://openstax.org/books/college-physics/pages/15-2-the-first-law-of-thermodynamics-and-some-simple-processes</a></li>
</ol>

등온 과정

일정한 온도에서 일어나는 열역학적 과정을 등온 과정이라고 합니다. 열은 열평형을 유지하기 위해 시스템 안으로 천천히 흘러 들어가거나 시스템 밖으로 흘러나갑니다. 물이 증기로 증발하거나 일정한 온도에서 물을 얼음으로 얼리는 등의 상 변화와 관련된 과정은 등온 과정의 예입니다.

이상기체는 등온 팽창이나 압축을 겪을 수도 있습니다.

예를 들어, 초기 부피가 V이고 압력이 p인 격리된 실린더 내부의 이상 기체 1몰을 생각해 보세요. 시스템에 추가된 열이 300K의 일정한 온도에서 가스의 준정적 팽창을 일으킨다고 가정합니다. 가스의 부피가 2V로 변경되면 시스템에 추가된 열의 양은 얼마입니까? ?

여기서 알려진 양은 가스의 몰수, 가스의 초기 및 최종 부피입니다. 알 수 없는 양인 열이 계산됩니다.

열역학 제1법칙에 따르면

<img alt="Equation1" src="/files/ftp_upload/13682/13682_Equation_PT_1.svg" style="text-align: center; height: 13px;" />

온도가 일정하므로 이 과정의 내부 에너지 변화는 0입니다. 따라서 시스템에 추가된 열은 시스템이 수행한 일과 같습니다.

<img alt="Equation2" src="/files/ftp_upload/13682/13682_Equation_PT_2.svg" style="text-align: center; height: 13px;" />

이제 등온 팽창 동안 이상 기체가 한 일은 다음과 같습니다.

<img alt="Equation3" src="/files/ftp_upload/13682/13682_Equation_PT_3.svg" style="text-align: center; height: 32px;" />

몰수, 기체 상수, 온도, 초기 부피, 기체의 최종 부피를 대입하면 수행된 일은 1728.85J입니다.

시스템이 한 일은 시스템에 추가된 열과 동일하므로 시스템을 등온적으로 2V로 팽창시키기 위해 시스템에 1728.85J의 열이 가해진 것으로 간주됩니다.

일정한 온도에서 발생하는 열역학적 과정을 등온 과정이라고 합니다. 열은 천천히 시스템 내부 또는 시스템 밖으로 흘러 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

The First Law of Thermodynamics

열역학 제1법칙

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 quasistatically at 300 K. The gas starts with 1 mole at volume V and pressure p. The volume then changes to 2V, and the heat added to the system must be found.

By the first law of thermodynamics, the change in internal energy is zero because the temperature stays constant. That means the heat added to the system equals the work done by the system. For an ideal gas in isothermal expansion, the work is calculated from the initial and final volume.

Substituting the number of moles, gas constant, temperature, and volumes gives a work value of 1728.85 J. Since the work done by the gas equals the heat added, 1728.85 J of heat is applied to expand the gas isothermally to 2V.

Isothermal Expansion and Heat Transfer

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

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...

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

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

Learn how isothermal processes keep temperature constant while heat equals work during ideal gas expansion, with phase change and cylinder examples.

Isothermal Expansion and Heat Transfer | 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.

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

New Jersey Student Learning Standards for Science

Physical Science

HS-PS3-1

Florida Department of Education

SC.912.P.10

SC.912.P.10.2

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-3.

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 ...

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 ...

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 ...

Enthalpy

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

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this ...

/files/media/science-education/science-education-thumbs/14702.jpg

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 ...

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 ...

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 and Work

Conservation of Momentum

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, ...

Entropy within the Cell

A living cell&#39;s primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics ...

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: Chemistry: Emphasis is on explaining the meaning of mathematical expressions used in the model. Focus is on basic algebraic expression or computations, systems of two or three components, and thermal energy.

What is Energy?

The universe is composed of matter in different forms, and all forms of matter contain energy. &#xA0;The different forms of energy on Earth originate from ...

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 ...

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

dual-nature-of-electromagnetic-em-radiation

Dual Nature of Electromagnetic (EM) Radiation

Electromagnetic (EM) radiation consists of electric and magnetic field components oscillating in planes perpendicular to each other and mutually ...

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 ...

Sound Waves

Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium&#39;s ...

Light as Energy

The energy required to carry out photosynthesis is light&#8212; typically electromagnetic radiation from the sun. The range of all possible wavelengths is ...

Quantifying Heat

Thermal Energy&#160;

Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a ...

Mechanism of heat transfer

Understanding heat transfer mechanisms is essential for understanding how our bodies maintain balance in different environmental conditions. When 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 ...

Design Consideration

While designing a structure, the considerations start with the ultimate strength of a material, which is determined through tests, measuring changes under ...

design-example-analyzing-capacity-contours-for-flood-risk-assessment

Design Example: Analyzing Capacity Contours for Flood Risk Assessment

Flood risk assessment involves careful planning and analysis to ensure the safety of communities near water retention structures. Capacity contours are a ...

design-example-calculating-safe-diameter-for-wind-exposed-disc

Design Example: Calculating Safe Diameter for Wind-Exposed Disc

Assessing safety in wind-exposed installations is crucial to preventing potential failures. This example explores the calculation and design adjustments ...

Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.  Clarification Statement: Chemistry: Emphasis is on both qualitative and quantitative evaluations of devices. Constraints could include use of renewable energy forms and efficiency. Focus of quantitative evaluations is limited to total output for a given input. Emphasis is on devices constructed with teacher approved materials. Examples of devices in chemistry could include hot/cold packs and batteries.

HS-PS3-3

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the ...

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the ...

Temperature and Thermal Equilibrium

Heat and temperature are essential concepts for everyone every day. The study of heat and temperature is part of an area of physics known as ...

Heat Engines

A heat engine is a device used to extract heat from a source and then convert it into mechanical work used for various applications. For example, a steam ...

Zeroth Law of Thermodynamics

Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. ...

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 ...

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 ...

le-chatelier-s-principle-changing-temperature

Le Chatelier's Principle: Changing Temperature

Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in ...

Constant Pressure Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process or to measure the heat transferred to or from a ...

Entropy

The Carnot Cycle

Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the ...

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: Physical Science, Physics and Chemistry: Emphasis is on analyzing data from student investigations and using mathematical thinking appropriate to the subject to describe the energy changes quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water.

Radioactivity and Nuclear Equations

Nuclear chemistry is the study of reactions that involve changes in nuclear structure. The nucleus of an atom is composed of protons and, except for ...

Types of Radioactivity

The most common types of radioactivity are &#945; decay, &#946; decay, &#947; decay, neutron emission, and electron capture.
Alpha (&#945;) decay is the ...

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10&#8722;15 meters, a nucleus is ...

Nuclear Binding Energy

The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect ...

Radioactive Decay and Radiometric Dating

Radioactivity is a spontaneous disintegration of an unstable nuclide and is a random process, as all the nuclei in the sample do not decay simultaneously. ...

Nuclear Fission

Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger ...

Nuclear Power

Controlled nuclear fission reactions are used to generate electricity. Any nuclear reactor that produces power via the fission of uranium or plutonium by ...

Nuclear Fusion

The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process ...

Nuclear Transmutation

Nuclear transmutation is the conversion of one nuclide into another. It can occur by the radioactive decay of a nucleus, or the reaction of a nucleus with ...

Biological Effects of Radiation

All radioactive nuclides emit high-energy particles or electromagnetic waves. When this radiation encounters living cells, it can cause heating, break ...

Evaluate the validity and reliability of claims in published materials about the viability of nuclear power as a source of alternative energy relative to other forms of energy (e.g., fossil fuels, wind, solar, geothermal).  Clarification Statement: Emphasis is on the trade-offs existing between the amount of energy produced, the types and amounts of pollution produced, safety, and cost.  Examples of published materials could include trade books, magazines, web resources, videos, and other passages that may reflect bias.

HS-PS3-6

Isothermal Expansion and Heat Transfer

Description

Transcript

Tags

More videos by Standards