Name: free expansion: pressure, volume, and temperature
Uploaded: 2023-04-30T12:32:36.000Z
Duration: 1 min 27 s
Channel: JoVE

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

Pressure and Volume in an Adiabatic Process

Consideriamo un volume di molecole d'aria che salgono nell'atmosfera. Poiché la pressione diminuisce con l'altitudine, le molecole d'aria cercano di mantenere la stessa pressione aumentando il loro volume in un processo adiabatico.
La variazione di energia interna è scritta in termini di capacità termica molare e riorganizzata.
L'uso della legge dei gas ideali, la differenziazione e la riorganizzazione dei termini danno un'espressione per il cambiamento di temperatura.
Equiparando le equazioni di variazione della temperatura ottenute dalla prima legge della termodinamica e dalla legge dei gas ideali e riorganizzando si ottiene un'equazione in termini di capacità termica molare.
Dividere per pV e utilizzare la relazione tra le capacità termiche molari. L'equazione può essere ulteriormente semplificata utilizzando il loro rapporto.
Dopo l'integrazione e utilizzando un'espressione matematica generale per i logaritmi, si ottiene la condizione affinché un gas ideale subisca un processo adiabatico in termini di pressione e volume.
Allo stesso modo, si possono scrivere le condizioni per i processi adiabatici in termini di temperatura-volume e pressione-temperatura.
Quindi, quando l'aria si espande, la temperatura scende come dato dalla condizione di temperatura-volume, condensandosi per formare nuvole.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson. PAGINE 640, 641</li>
	<li>Walker, Jearl (2007). Halliday e Resnick Fondamenti di fisica. Wiley. Pagine 573-574</li>
</ol>

pressione e volume in un processo adiabatico

L'espansione libera di un gas è un processo adiabatico. Tuttavia, ci sono poche differenze tra l'espansione libera e l'espansione adiabatica. Durante l'espansione libera, non viene svolto alcun lavoro e non vi è alcuna variazione nell'energia interna. Ma, per un'espansione adiabatica, viene svolto lavoro e vi è una variazione nell'energia interna. Durante un processo adiabatico, la relazione tra la pressione e il volume è ottenuta dalla condizione per il processo adiabatico, cioè:

<img alt="Equation1" src="/files/ftp_upload/13688/13688_PT Equation_1.svg" style="text-align: center; height: 13px;" />

Tuttavia, per un processo di espansione libera, questa condizione non vale anche se l'espansione è adiabatica. Inoltre, in un processo di espansione libera, il gas è in uno stato di equilibrio solo nei punti iniziale e finale. Pertanto, su un diagramma pV, possono essere tracciati solo quei punti iniziali e finali, non l'espansione stessa. Oltre a ciò, la temperatura iniziale e finale per un processo adiabatico sono correlate dall'espressione:

<img alt="Equation2" src="/files/ftp_upload/13688/13688_PT Equation_2.svg" style="text-align: center; height: 18px;" />

Ma per l'espansione libera, non vi è alcuna variazione nell'energia interna; quindi, le temperature iniziale e finale sono uguali. Pertanto, invece dell'equazione sopra, abbiamo:

<img alt="Equation3" src="/files/ftp_upload/13688/13688_PT Equation_3.svg" style="text-align: center; height: 13px;" />

Dall'espressione per la temperatura, gli stati iniziali e finali di un'espansione libera giacciono sulla stessa isoterma in un diagramma pV. Ora, se si assume che il gas sia ideale, allora, poiché non vi è alcuna variazione nella temperatura, non può esserci alcuna variazione nel prodotto di pressione e volume. Pertanto, per l'espansione libera, la pressione e il volume possono essere espressi come:

<img alt="Equation4" src="/files/ftp_upload/13688/13688_PT Equation_4.svg" style="text-align: center; height: 13px;" />

Pressione e volume in un processo adiabatico

L'espansione libera di un gas è un processo adiabatico. Tuttavia, ci sono poche differenze tra l'espansione libera e l'espansione adiabatica. Durante l'espansione libera, ...

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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 adiabatic. The gas is in equilibrium only at the start and the end of free expansion. Because of that, only the initial and final points can be shown on a pV diagram, not the path of the expansion.

The temperature behavior is also different. For adiabatic expansion, the initial and final temperatures are linked by an equation. For free expansion, the internal energy stays the same, so the initial and final temperatures are equal. This means the two states lie on the same isotherm, or constant-temperature line, on a pV diagram.

If the gas is ideal, a constant temperature means the product of pressure and volume does not change. So for free expansion, pressure and volume can be written with the same value of pV at the initial and final states. This makes free expansion a useful case for comparing adiabatic behavior with a process that changes volume without changing internal energy.

Free Expansion: Pressure, Volume, and Temperature

free-expansion-pressure-volume-temperature

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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Net Work in a Cyclic Thermodynamic Process

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isothermal processes

Isothermal Expansion and Heat Transfer

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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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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

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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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...

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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...

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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...

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Explore how free expansion differs from adiabatic expansion, including no work done, unchanged internal energy, equal temperatures, and pV diagram behavior.

Free Expansion: Pressure, Volume, and Temperature | JoVE K12

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Free Expansion: Pressure, Volume, and Temperature

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