Name: how internal energy changes in gas systems
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 29 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

Energy

PHYS.PS3.7

Internal Energy

Die innere Energie eines Systems kann als die Summe der kinetischen und potentiellen Energien aller einzelnen Atome im System definiert werden.
Betrachten wir ein System aus einem monoatomaren idealen Gas. Wenn das Gas bei konstantem Volumen erhitzt wird, steigt die kinetische Energie der Atome, aber da es keine Wechselwirkung zwischen den Atomen gibt, bleibt ihre potentielle Energie Null.
Daher hängt die innere Energie von der durchschnittlichen kinetischen Energie der monoatomaren Atome ab. Sie wird ausgedrückt als drei über zwei NkBT, wobei N die Anzahl der Gasatome, kB die Boltzmann-Konstante und T ihre Temperatur ist. Die innere Energie eines idealen Gases bei konstantem Volumen hängt also nur von der Temperatur ab.
Die innere Energie eines Systems ist eine Zustandsfunktion. Siedendes Wasser, das auf Raumtemperatur abgekühlt wurde, hat die gleiche innere Energie wie Wasser, das durch Schmelzen von Eis auf Raumtemperatur gewonnen wird.
Die innere Energie hängt also nur vom Zustand des Systems ab, nicht aber vom Weg, um sie zu erhalten. Daher ist es pfadunabhängig.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson. S. 629.</li>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion] S. 115–116. Abgerufen von <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>

innere energie

Die innere Energie eines thermodynamischen Systems ist die Summe der kinetischen und potentiellen Energien aller Moleküle oder Einheiten im System. Die kinetische Energie eines einzelnen Moleküls umfasst Beiträge aufgrund seiner Rotation und Vibration sowie seine translatorische Energie. Die potentielle Energie ist nur mit den Wechselwirkungen zwischen einem Molekül und den anderen Molekülen des Systems verbunden. Weder der Ort noch die Bewegung des Systems sind bezüglich der inneren Energie von Bedeutung.

Betrachten Sie ein ideales einatomiges Gas. Hier besteht jedes Molekül aus einem einzelnen Atom. Folglich gibt es keine rotations- oder vibrationskinetische Energie. Darüber hinaus gibt es keine zwischenatomaren Wechselwirkungen, daher wird angenommen, dass die potentielle Energie null ist. Die innere Energie ist daher nur das Ergebnis der translatorischen kinetischen Energie. Daher ergibt sich die innere Energie eines idealen Gases einfach aus der Anzahl der Moleküle multipliziert mit der durchschnittlichen kinetischen Energie pro Molekül. So ergibt sich für n Mol eines idealen einatomigen Gases die innere Energie wie folgt:

<img alt="Equation1" src="/files/ftp_upload/13678/13678_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

Es ist ersichtlich, dass die innere Energie einer bestimmten Menge eines idealen einatomigen Gases von der Temperatur abhängt und unabhängig vom Druck und Volumen des Gases ist. Für andere Systeme kann die innere Energie nicht so einfach ausgedrückt werden. Eine Erhöhung der inneren Energie kann jedoch oft mit einer Erhöhung der Temperatur in Verbindung gebracht werden.

Im Allgemeinen, wenn eine Wärmemenge Q zu einem System hinzugefügt wird und das System während des Prozesses keine Arbeit verrichtet, nimmt die innere Energie um einen Betrag Q zu. Wenn ein System Arbeit W leistet, indem es sich gegen seine Umgebung ausdehnt und kein Wärme während des Prozesses zugeführt wird, verlässt Energie das System und die innere Energie nimmt ab. Während Q und W vom Weg abhängen, hängt die Änderung der inneren Energie eines Systems während eines beliebigen thermodynamischen Prozesses nur von den Anfangs- und Endzuständen ab, nicht vom Weg, der von einem zum anderen Zustand führt.

Innere Energie

Die innere Energie eines thermodynamischen Systems ist die Summe der kinetischen und potentiellen Energien aller Moleküle oder Entitäten im System. Die kinetische ...

Education

Lehre

JoVE Core

Physik

Unit 1

Einheit 1

The First Law of Thermodynamics

Der erste Hauptsatz der Thermodynamik

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 vibrational kinetic energy. There are also no interatomic interactions, so the potential energy is taken as zero.

In that case, the internal energy comes only from translational kinetic energy. So the internal energy of an ideal gas depends on the number of molecules and the average kinetic energy per molecule. For n moles of an ideal monatomic gas, the internal energy is set by temperature. It does not depend on the gas pressure or volume.

For other systems, internal energy is not so easy to write in a simple form. Even so, a rise in internal energy is often linked to a rise in temperature. When heat Q is added to a system and the system does no work, the internal energy increases by the same amount. When a system does work W by expanding against its surroundings and no heat is added, energy leaves the system and the internal energy decreases.

Heat Q and work W depend on the path taken during the process. The change in internal energy does not. It depends only on the initial and final states of the system.

How Internal Energy Changes in Gas Systems

how-internal-energy-changes-in-gas-systems

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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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...

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Path Dependence in Gas Work

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internal energy

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

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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...

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Net Work in a Cyclic Thermodynamic Process

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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...

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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...

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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

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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

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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

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

Explore how internal energy depends on molecular motion, temperature, heat, and work in ideal monatomic gases and other thermodynamic systems.

How Internal Energy Changes in Gas Systems | JoVE K12

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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.

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New Jersey Student Learning Standards for Science

Physical Science

HS-PS3-4

Arizona Science Standards

HS.P4

HS.P4U1.8

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HS+Phy.P4U1.6

Florida Department of Education

SC.912.P.10

SC.912.P.10.2

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South Carolina College and Career Ready Science Standards

P-PS3-3

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New York State Science Learning Standards

HS. Energy

HS-PS3-3.

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Kinetic Energy - I

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Identify and calculate different types of energy and their transformations (thermal, kinetic, potential, including magnetic and electrical potential energies) from one form to another in a system. Identify and calculate different types of energy and their transformations (thermal, kinetic, potential, including magnetic and electrical potential energies) from one form to another in a system. EXPLANATION:  In 6.PS3 students were introduced to the various types of energy and mechanisms for their transformations. Students should now be able to quantify the total energy of a system as well as quantify each different type of energy in a system. Energy is an abstract concept that does not have a physical form. It is a substance-like quantity that is recognized to be conserved as a system changes. Calculations present an opportunity to observe that potential energies are due to the positions of objects within a field, while kinetic energy is based on an object’s mass and motion. Students can evaluate the total energy of a system by imagining that there are different types of energy storage accounts, just as money can be stored in different accounts. Energy can transferred into or out of any of these accounts. Three different processes can account for all energy changes: working, heating, and radiating. In energy storage due to field effects, such as gravitational or electrostatic fields, the field itself stores the potential energy and not the object in the field.

PHYS.PS3.1

What is Energy?

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Heat Flow and Specific Heat

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PHYS.PS3.2

Quantifying Heat

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Energy Diagrams - I

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Use the principle of energy conservation and mathematical representations to quantify the change in energy of one component of a system when the energy that flows in and out of the system and the change in energy of the other components is known.         Use the principle of energy conservation and mathematical representations to quantify the change in energy of one component of a system when the energy that flows in and out of the system and the change in energy of the other components is known.         EXPLANATION:  In PHYS.PS3.1 students quantify the various types of energy and consider methods for energy transfer. If a student is able to evaluate the total energy of a system, such evaluations before and after a change to a system provide a mechanism to show that energy of a system has been conserved. For example, students might use pie charts to show the distribution of the total energy. For an object about to freefall, the pie chart might be 100% gravitational potential energy. Mid-descent, the energy might be half gravitational potential energy and half kinetic energy. After colliding with the ground, the total energy may have decreased, which can be represented as heat energy lost from the pie chart.

PHYS.PS3.3

Linear Momentum

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Impulse

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Types Of Collisions - I

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PHYS.PS3.4

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PHYS.PS3.5

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Define power and solve problems involving the rate of energy production or consumption (P=∆E/∆t). Explain and predict changes in power consumption based on changes in energy demand or elapsed time. Investigate power consumption and power production systems in common use.  Define power and solve problems involving the rate of energy production or consumption (P=∆E/∆t). Explain and predict changes in power consumption based on changes in energy demand or elapsed time. Investigate power consumption and power production systems in common use. EXPLANATION:  This standard pairs well with PHYS.PS3.6. Students should understand that a given task will require a certain minimum amount of energy. In accordance with the work-energy theorem, this would be described as work done on the system. Power incorporates a rate element into this discussion. An object can be lifted to an identical height by two different mechanisms. The total energy input into the system (the object and Earth’s gravitational field) will be the same in either case. However, if one mechanism for lifting the object does this in a smaller amount of time, it is said to be more powerful. Students may compare two different devices that accomplish the same task, but have different power ratings and explain the impact of the different power ratings on how the devices are used. For example, two microwaves might both pop a bag of popcorn, but a more powerful microwave might do it faster or be more likely to burn the popcorn at recommended time settings.

PHYS.PS3.6

How Internal Energy Changes in Gas Systems

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