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

Rozważmy butlę z gazem doskonałym o objętości Vo pod ciśnieniem po, wyposażoną w tłok bez tarcia przymocowany do masy. Tłok pozostaje nieruchomy, gdy ciśnienie jest w równowadze.
Jeśli masa zmniejszy się o połowę, ciśnienie zewnętrzne na tłoku zmniejszy się proporcjonalnie. Wyższe ciśnienie wewnętrzne gazu popycha tłok do przodu, aż do osiągnięcia nowej równowagi.
Zwiększa się objętość gazu. System osiąga nowy stan termodynamiczny wykonując pracę.
Załóżmy, że ten sam stan końcowy osiąga się poprzez zmniejszenie masy w dwóch etapach. Początkowo ciśnienie spada do 0,75po, a wykonana praca jest reprezentowana przez obszar pod drugą krzywą.
Zmniejszając dalej masę w drugim etapie, praca wykonana przez gaz jest równa powierzchni pod trzecią krzywą. Dlatego całkowita praca wykonana przez gaz w drugim procesie jest sumą obszarów pod dwiema krzywymi.
W związku z tym praca wykonywana przez gaz jest różna dla różnych procesów, a zatem jest to funkcja zależna od ścieżki.

<ol>
 <li>Young, H.D., Freedman, R.A. Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson. 628 (2012).</li>
 <li>Protokół OpenStax. Fizyka Uniwersytecka Vol.2. Pg 110 [Wersja internetowa]. Źródło: <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>

Ścieżka między stanami termodynamiki

Rozważ dwa procesy termodynamiczne z udziałem gazu doskonałego, które są reprezentowane przez ścieżki AC i ABC na rysunku 1:

<img alt="Równanie1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;" />

W pierwszym procesie dla ścieżki A do C gaz utrzymuje się w stałej temperaturze T. Ulega ekspansji z tomu V1 do V2.

Pracę wykonaną przez gaz doskonały wyraża się jako

<img alt="Równanie1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;" />

Zastępując ciśnienie jako nRT/V z równania gazu doskonałego i całkując wyrazy, otrzymuje się pracę wykonaną przez gaz doskonały w stałej temperaturze jako

<img alt="Równanie2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;" />

W drugim procesie, dla ścieżki A do B, gaz doskonały jest najpierw rozprężany z objętości V1 do V2 przy stałym ciśnieniu p1 poprzez zastosowanie ciepła. Następnie gaz schładza się do stałej objętości V2 wzdłuż ścieżki B do C tak, że jego ciśnienie spada do p2.

W przypadku ścieżki A do B praca jest wykonywana pod stałym ciśnieniem, dlatego

<img alt="Równanie3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;" />

W przypadku ścieżki B do C, ponieważ objętość pozostaje stała, gaz nie wykonuje żadnej pracy, a otoczenie nie wykonuje nad nim żadnej pracy. Dlatego całkowita praca wykonana przez gaz w tym procesie jest taka sama, jak praca wykonana na ścieżce A do B.

W obu procesach gaz rozpręża się z objętości V1 do objętości V2 tak, że jego ciśnienie zmienia się z p1 na p2. Jednak praca wykonana w obu procesach jest inna. Dowodzi to, że praca wykonana przez system zależy od ścieżki.

Rozważmy dwa procesy termodynamiczne z udziałem gazu doskonałego, które są reprezentowane przez ścieżki AC i ABC na rysunku 1:

W pierwszym procesie dla ścieżki A do ...

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

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

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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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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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HS-PS3-5

Path Dependence in Gas Work

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