Name: path dependence in gas work
Uploaded: 2023-04-30T12:31:19.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Path Between Thermodynamics States

Рассмотрим цилиндр с идеальным газом объема Vo при давлении po, оснащенный поршнем без трения, прикрепленным к массе. Поршень остается неподвижным, пока давление находится в равновесии.
Если масса уменьшается вдвое, то внешнее давление на поршень уменьшается пропорционально. Более высокое внутреннее давление газа толкает поршень вперед до тех пор, пока не будет достигнуто новое равновесие.
Объем газа увеличивается. Система переходит в новое термодинамическое состояние, выполняя работу.
Предположим, что такое же конечное состояние достигается за счет уменьшения массы в два этапа. Первоначально давление снижается до 0,75po, а проделанная работа представлена областью под второй кривой.
При дальнейшем уменьшении массы на втором этапе работа, выполняемая газом, равна площади под третьей кривой. Таким образом, общая работа, выполняемая газом во втором процессе, представляет собой сумму площадей под двумя кривыми.
Таким образом, работа, выполняемая газом, различна для разных процессов, и, следовательно, это функция, зависящая от траектории.

<ol>
 <li>Янг, Х.Д., Фридман, Р.А. Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. 628 (2012).</li>
 <li>OpenStax. Университетская физика Том 2. стр. 110 [Веб-версия]. Получено из <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>

Путь между состояниями термодинамики

Рассмотрим два термодинамических процесса, связанных с идеальным газом, представленных путями AC и ABC на рисунке 1.

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;" />

В первом процессе по пути A до C газ находится при постоянной температуре T. Он расширяется от объема V1 до V2.

.



Работа, совершённая идеальным газом, выражается следующим образом:

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;" />

Заменяя давление на nRT/V из уравнения идеального газа и интегрируя члены, получаем, что совершенная идеальным газом при постоянной температуре работа равна:

<img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;" />

Во втором процессе по пути A до B идеальный газ сначала расширяется от объема V1 до V2 при постоянном давлении p1 , путем подачи тепла. Затем газ охлаждается при постоянном объеме V2 по пути B до C, так что его давление падает до p2.

Для пути A до B работа совершается при постоянном давлении, поэтому:

<img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;" />

Для пути B до C, так как объём остается постоянным, работа не совершается газом и не совершается над газом окружающей средой. Поэтому общая работа, совершенная газом в этом процессе, такая же, как работа, совершённая по пути A до B.

В обоих процессах газ расширяется от объёма V1 до объема V2, так что его давление изменяется с p1 до p2. Однако работа, совершенная в обоих процессах, различается. Это доказывает, что совершённая работа системой зависит от пути.

Рассмотрим два термодинамических процесса с участием идеального газа, которые представлены траекториями AC и ABC на рисунке 1:

В первом процессе для пути А в ...

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

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 isothermal process is obtained.

Along path ABC, the gas follows two steps. First, it expands from V1 to V2 at constant pressure p1 by applying heat. Then it is cooled at constant volume V2, and its pressure drops to p2. During the constant-pressure step AB, work is done by the gas. During the constant-volume step BC, no work is done because the volume does not change.

The total work for path ABC is therefore the same as the work done during AB. Even though both paths connect the same start and end states and the pressure changes from p1 to p2, the work values are different. This shows that work done by a system is path-dependent.

Path Dependence in Gas Work

thermodynamic systems

Open, Closed, and Isolated Systems

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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...

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adiabatic processes for an ideal gas

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key terms and concepts

Compare two ideal-gas paths between the same states and see why an isothermal route and a constant-pressure-plus-volume route give different work values.

Path Dependence in Gas Work | JoVE K12

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Path Dependence in Gas Work

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