Name: two gas paths to the same volume
Uploaded: 2023-09-18T17:11:15.000Z
Duration: 1 min 24 s
Channel: JoVE

K12 Standards

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High School

Physics

Energy

PHYS.PS3.7

Heat and Free Expansion

Die Arbeit eines thermodynamischen Systems ist unter allen Bedingungen pfadabhängig.
Stellen Sie sich ein System aus zwei Zylindern vor, die mit einem Druckventil verbunden sind. Zunächst ist Zylinder A mit einem idealen Gas gefüllt, während Zylinder B leer ist
Am Heizzylinder A nimmt das Gas die Wärme auf und erhöht vorübergehend den Druck im Zylinder A, wodurch das Druckventil geöffnet wird. Das Gas dehnt sich isotherm in Zylinder B aus, wodurch der Druck in Zylinder A verringert wird.
Unter Berücksichtigung vernachlässigbarer Gaspartikel in Verbindungsrohren entspricht das endgültige Gasvolumen der Summe der Gasmengen in beiden Zylindern.
Hier werden die Arbeiten am Druckventil aufgrund der Erwärmung des Gases erledigt.
Betrachten Sie in einem anderen Prozess das gleiche System in seinem Ausgangszustand, isoliert von seiner Umgebung, so dass keine Wärme ausgetauscht wird.
Wird das Ventil entfernt, durchläuft das Gas eine schnelle freie Expansion in Zylinder B und erreicht schließlich das gleiche Endvolumen wie im ersten Prozess.
Während dieser Expansion verschieben sich keine Grenzen, was darauf hindeutet, dass die Arbeit, die das Gas unter freier Expansion leistet, Null ist.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson. Seite 628.</li>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion] S. 112-115. 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>

wärme und freie expansion

Die von einem thermodynamischen System geleistete Arbeit hängt nicht nur von den Anfangs- und Endzuständen ab, sondern auch von den Zwischenzuständen – das heißt von der Strecke. Ähnlich wie die Arbeit durchläuft ein thermodynamisches System beim Hinzufügen von Wärme eine Zustandsänderung, und der erreichte Zustand hängt vom Weg vom Anfangszustand zum Endzustand ab. Betrachten wir einen idealen Gaszylinder, der mit einem Kolben ausgestattet ist. Wenn der Zylinder bei konstanter Temperatur erwärmt wird, absorbieren die Gasmoleküle Energie und dehnen sich langsam auf kontrollierte Weise isotherm aus. Dies drückt den Kolben nach oben, und das Gas erreicht schließlich das endgültige Volumen. Hierbei wird Arbeit vom Gas aufgrund der Wärmeausdehnung auf den Kolben geleistet.

Das Gas kann dasselbe Endvolumen auch durch ein anderes Verfahren erreichen. Betrachten wir einen Zylinder, der von isolierenden Wänden umgeben ist und durch eine dünne, abnehmbare Trennwand geteilt ist. Die untere Kammer ist mit derselben Menge an Gas bei derselben Temperatur gefüllt, sodass der Ausgangszustand derselbe ist wie oben beschrieben. Wenn die Trennwand entfernt wird, unterliegt das Gas einer schnellen, unkontrollierten Ausdehnung, ohne dass Wärme durch die isolierenden Wände gelangt, und erreicht dasselbe Endvolumen wie im obigen Fall. Hierbei leistet das Gas bei dieser Ausdehnung keine Arbeit, da es nicht gegen irgendwas stößt, das sich bewegt. Diese unkontrollierte Ausdehnung eines Gases in ein Vakuum wird als freie Expansion bezeichnet.

Experimentell gesehen gibt es bei einer freien Expansion eines idealen Gases keine Temperaturänderung. Das bedeutet, dass der Endzustand des Gases gleich bleibt. Die Zwischenzustände (Drücke und Volumina) während des Übergangs vom Anfangs- zum Endzustand sind in den beiden Fällen vollständig unterschiedlich. Somit stellt es zwei verschiedene Wege dar, die denselben Anfangs- und Endzustand verbinden.

Wärme und Freie Expansion

Die Arbeit, die ein thermodynamisches System leistet, hängt nicht nur vom Anfangs- und Endzustand ab, sondern auch von den Zwischenzuständen, also vom Weg. ...

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The First Law of Thermodynamics

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KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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. This pushes the piston upward, and the gas reaches the final volume. During this expansion, the gas does work on the piston.

The second case uses a cylinder with insulating walls and a thin removable partition. The lower part contains the same amount of gas at the same temperature, so the initial state matches the first example. When the partition is removed, the gas expands quickly and without control. No heat passes through the insulating walls, and the gas does not push against anything that moves, so no work is done.

This sudden expansion into a vacuum is called free expansion. For an ideal gas, experiments show no change in temperature during free expansion. That means the final state stays the same in both cases. Even so, the pressure and volume during the change are very different, so the two processes follow different paths between the same starting and ending states.

Two Gas Paths to the Same Volume

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

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

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.

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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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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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isothermal processes

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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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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

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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 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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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...

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thermodynamic potentials

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key terms and concepts

Compare isothermal expansion and free expansion in an ideal gas. See how heat, work, and path affect the same final volume in thermodynamics.

Two Gas Paths to the Same Volume | JoVE K12

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New Jersey Student Learning Standards for Science

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SC.912.P.10.2

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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

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Quantifying Heat

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Linear Momentum

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PHYS.PS3.4

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Construct an argument based on qualitative and quantitative evidence that relates the change in temperature of a substance to its mass and heat energy added or removed from a system. Construct an argument based on qualitative and quantitative evidence that relates the change in temperature of a substance to its mass and heat energy added or removed from a system.  EXPLANATION: Two different materials will undergo different degrees of temperature change even with the same amount of energy added to each. Heat capacity is a ratio (the slope of a temperature vs. heat added) that describes the change in temperature of a sample dependent on the amount of heating. Empirical determination of the heat capacity of a substance requires that both phase and mass of the substance are constants. Students can utilize proportional reasoning in the design of a second portion of this experiment to determine the effect of mass on temperature change.

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

Two Gas Paths to the Same Volume

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