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

Рассмотрим объем молекул воздуха, поднимающихся в атмосферу. Поскольку давление уменьшается с высотой, молекулы воздуха пытаются поддерживать то же давление, увеличивая свой объем при адиабатическом процессе.
Внутреннее изменение энергии записывается в терминах молярной теплоемкости и перестраивается.
Использование закона идеального газа, его дифференцирование и перестановка членов дает выражение для изменения температуры.
Приравнивание уравнений изменения температуры, полученных из первого начала термодинамики и закона идеального газа, и перестановки дает уравнение в терминах молярной теплоемкости.
Разделите поперек на пВ и используйте соотношение между молярными теплоемкостью. Уравнение можно еще больше упростить с помощью их соотношения.
Путем интегрирования и использования общего математического выражения для логарифмов получается условие для того, чтобы идеальный газ претерпел адиабатический процесс в терминах давления и объема.
Аналогично можно записать условия адиабатических процессов в терминах температура-объем и давление-температура.
Таким образом, когда воздух расширяется, температура падает в соответствии с температурно-объемным условием, конденсируясь с образованием облаков.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. С. 640, 641</li>
	<li>Уокер, Джерл (2007). Холлидей и Резник Основы физики. Вайли. С. 573-574</li>
</ol>

Давление и объем в адиабатическом процессе

Свободное расширение газа является адиабатическим процессом. Однако между свободным и адиабатическим расширением есть несколько различий. Во время свободного расширения не выполняется никакая работа, и не происходит изменение внутренней энергии. Но во время адиабатического расширения выполняется работа и происходит изменение внутренней энергии. Во время адиабатического процесса соотношение между давлением и объёмом определяется из условия для адиабатического процесса:

<img alt="Equation1" src="/files/ftp_upload/13688/13688_PT Equation_1.svg" style="text-align: center; height: 13px;" />

Однако для свободного расширения это условие не выполняется, даже если расширение является адиабатическим. Кроме того, в процессе свободного расширения, газ находится в состоянии равновесия только в начальной и конечной точках. Таким образом, на диаграмме pV можно отметить только эти начальные и конечные точки, а не само расширение. В дополнение к этому, начальная и конечная температура для адиабатического процесса связаны выражением:

<img alt="Equation2" src="/files/ftp_upload/13688/13688_PT Equation_2.svg" style="text-align: center; height: 18px;" />

Однако для свободного расширения нет изменения внутренней энергии, поэтому начальная и конечная температуры равны. Таким образом, вместо вышеприведенного уравнения мы имеем:

<img alt="Equation3" src="/files/ftp_upload/13688/13688_PT Equation_3.svg" style="text-align: center; height: 13px;" />

Из выражения для температуры начальное и конечное состояние свободного расширения лежат на одной изотерме на диаграмме pV . Теперь, если предположить, что газ является идеальным, то, поскольку нет изменения температуры, не может быть изменения произведения давления и объёма. Следовательно, для свободного расширения давление и объём могут быть выражены как:

<img alt="Equation4" src="/files/ftp_upload/13688/13688_PT Equation_4.svg" style="text-align: center; height: 13px;" />

Свободное расширение газа является адиабатическим процессом. Тем не менее, между свободным расширением и адиабатическим расширением есть несколько различий. Во время свободного расширения...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

The First Law of Thermodynamics

Первый закон термодинамики

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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Heat, Work, and Internal Energy

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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...

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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...

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

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

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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...

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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...

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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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