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

考虑大气中一团上升的空气分子。随着海拔升高，压力降低，空气分子会通过绝热过程增大其体积，以试图维持相同的压力。
用摩尔热容表示内能变化，并进行重新整理。
利用理想气体状态方程，对其求导并重新整理各项，可得到温度变化的表达式。
将由热力学第一定律和理想气体定律得到的温度变化方程进行联立并重新整理，可得到以摩尔热容表示的方程。
两边同时除以 pV，并利用摩尔热容之间的关系。该方程可进一步通过它们的比值进行简化。
通过积分并使用对数的一般数学表达式，可得到理想气体经历绝热过程时以压强和体积表示的条件。
类似地，绝热过程的条件可以用温度-体积和压力-温度关系来表示。
因此，当空气膨胀时，根据温度-体积关系，温度会下降，从而凝结形成云。

<ol>
	<li>Young， HD 和 Freedman， RA （2012）。大学物理与现代物理。加利福尼亚州旧金山:皮尔逊。第 640、641 页</li>
	<li>沃克，杰尔 （2007）。Halliday 和 Resnick 物理学基础。威利。第 573-574 页</li>
</ol>

绝热过程中的压力和体积

气体的自由膨胀是一个绝热过程。 然而，自由膨胀和绝热膨胀之间几乎没有区别。 自由膨胀时不做功，内能也没有变化。 但是，对于绝热膨胀，功已经完成，并且内能发生变化。 在绝热过程中，由绝热过程的条件得到压力与体积的关系，即：  <img alt="Equation1" src="/files/ftp_upload/13688/13688_PT Equation_1.svg" style="text-align: center; height: 13px;"> 然而，对于自由膨胀过程，即使膨胀是绝热的，这个条件也不成立。 此外，在自由膨胀过程中，气体仅在初始点和最终点处于平衡状态。 因此，在 pV 图上，只能绘制那些初始点和最终点，而不能绘制扩展本身。 除此之外，绝热过程的初始温度和最终温度通过以下表达式相关： <img alt="Equation2" src="/files/ftp_upload/13688/13688_PT Equation_2.svg" style="text-align: center; height: 18px;"> 但对于自由膨胀，内能没有变化； 因此，初始温度和最终温度相等。 因此，我们有 <img alt="Equation3" src="/files/ftp_upload/13688/13688_PT Equation_3.svg" style="text-align: center; height: 13px;"> 根据温度表达式，自由膨胀的初始状态和最终状态位于 pV 图中的同一条等温线上。 现在，如果假设气体是理想的，那么，由于温度没有变化，压力和体积的乘积也不会发生变化。 因此对于自由膨胀，压力和体积可以表示为： <img alt="Equation4" src="/files/ftp_upload/13688/13688_PT Equation_4.svg" style="text-align: center; height: 13px;">

气体的自由膨胀是一个绝热过程。然而，自由膨胀与绝热膨胀之间存在一些差异。在自由膨胀过程中，……

Education

教育

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Physics

物理学

Unit 1

第一单元

The First Law of Thermodynamics

热力学第一定律

KEY TERMS AND CONCEPTS

关键术语与概念

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

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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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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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