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

K12 Standards

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

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

Pressure and Volume in an Adiabatic Process

Weźmy pod uwagę objętość cząsteczek powietrza unoszących się w atmosferze. Ponieważ ciśnienie spada wraz z wysokością, cząsteczki powietrza starają się utrzymać to samo ciśnienie, zwiększając swoją objętość w procesie adiabatycznym.
Wewnętrzna zmiana energii jest zapisywana w kategoriach molowej pojemności cieplnej i przestawiana.
Użycie prawa gazu doskonałego, rozróżnienie go i przegrupowanie terminów daje wyrażenie na zmianę temperatury.
Zrównanie równań zmiany temperatury uzyskanych z pierwszej zasady termodynamiki i prawa gazu doskonałego oraz przegrupowanie daje równanie pod względem molowej pojemności cieplnej.
Podziel przez pV i wykorzystaj zależność między molowymi pojemnościami cieplnymi. Równanie można jeszcze bardziej uprościć za pomocą ich stosunku.
Po całkowaniu i użyciu ogólnego wyrażenia matematycznego dla logarytmów, uzyskuje się warunek, aby gaz doskonały został poddany procesowi adiabatycznemu pod względem ciśnienia i objętości.
Podobnie można zapisać warunki dla procesów adiabatycznych pod względem temperatury-objętości i ciśnienia-temperatury.
Tak więc, gdy powietrze się rozszerza, temperatura spada zgodnie z warunkiem temperatura-objętość, kondensując się, tworząc chmury.

<ol>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson. STR. 640, 641</li>
	<li>Walker, Jearl (2007). Halliday i Resnick Podstawy fizyki. Wiley. Strony 573-574</li>
</ol>

ciśnienie i objętość w procesie adiabatycznym

Swobodne rozprężanie gazu jest procesem adiabatycznym. Istnieje jednak kilka różnic między swobodnym rozszerzaniem a rozszerzaniem adiabatycznym. Podczas swobodnego rozszerzania nie jest wykonywana żadna praca i nie następuje zmiana energii wewnętrznej. Jednak w przypadku ekspansji adiabatycznej praca zostaje wykonana i następuje zmiana energii wewnętrznej. Podczas procesu adiabatycznego zależność między ciśnieniem i objętością uzyskuje się z warunku procesu adiabatycznego, to znaczy:

<img alt="Equation1" src="/files/ftp_upload/13688/13688_PT Equation_1.svg" style="text-align: center; height: 13px;" />

Jednakże w przypadku procesu swobodnego rozprężania warunek ten nie obowiązuje, nawet jeśli rozprężanie jest adiabatyczne. Również w procesie swobodnego rozprężania gaz znajduje się w stanie równowagi tylko w punkcie początkowym i końcowym. Zatem na wykresie pV można wykreślić tylko punkty początkowe i końcowe, a nie samą ekspansję. Oprócz tego początkowa i końcowa temperatura procesu adiabatycznego są powiązane wyrażeniem

<img alt="Equation2" src="/files/ftp_upload/13688/13688_PT Equation_2.svg" style="text-align: center; height: 18px;" />

Ale w przypadku swobodnej ekspansji energia wewnętrzna nie ulega zmianie; stąd temperatura początkowa i końcowa są równe. Zatem zamiast powyższego równania mamy

<img alt="Equation3" src="/files/ftp_upload/13688/13688_PT Equation_3.svg" style="text-align: center; height: 13px;" />

Z wyrażenia na temperaturę wynika, że ​​początkowy i końcowy stan swobodnej ekspansji leżą na tej samej izotermie na diagramie pV . Jeśli przyjmiemy, że gaz jest idealny, to skoro nie ma zmiany temperatury, nie może też nastąpić zmiana iloczynu ciśnienia i objętości. Stąd w przypadku swobodnego rozszerzania ciśnienie i objętość można wyrazić jako,

<img alt="Equation4" src="/files/ftp_upload/13688/13688_PT Equation_4.svg" style="text-align: center; height: 13px;" />

Ciśnienie i objętość w procesie adiabatycznym

Swobodne rozszerzanie się gazu jest procesem adiabatycznym. Istnieje jednak kilka różnic między swobodną ekspansją a ekspansją adiabatyczną. Podczas swobodnej rozbudowy ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

The First Law of Thermodynamics

Pierwsza zasada termodynamiki

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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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cyclic processes and isolated systems

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

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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...

heat capacities of an ideal gas iii

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

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

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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...

key terms and concepts

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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