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

질량에 마찰이 없는 피스톤이 부착된 po의 압력에서 부피 Vo의 이상 가스를 가진 실린더를 고려하십시오. 피스톤은 압력이 평형 상태에 있는 동안 정지 상태를 유지합니다.
질량이 절반으로 감소하면 피스톤에 가해지는 외부 압력이 비례적으로 감소합니다. 가스의 내부 압력이 높을수록 새로운 평형에 도달할 때까지 피스톤을 앞으로 밀어냅니다.
가스량이 증가합니다. 시스템은 작업을 수행하여 새로운 열역학 상태에 도달합니다.
두 단계에서 질량을 줄여 동일한 최종 상태를 달성한다고 가정합니다. 처음에는 압력이 0.75po로 감소하고 완료된 작업은 두 번째 곡선 아래의 영역으로 표시됩니다.
두 번째 단계에서 질량을 더 줄이면 가스가 수행 한 작업은 세 번째 곡선 아래의 면적과 같습니다. 따라서 두 번째 프로세스에서 가스가 수행한 총 작업은 두 곡선 아래 영역의 합입니다.
따라서 가스가 수행하는 작업은 프로세스마다 다르므로 경로 종속 함수입니다.

<ol>
 <li>Young, H.D., Freedman, R.A. 현대 물리학을 가진 대학 물리학. 샌프란시스코, 캘리포니아 : 피어슨. 628 (2012년).</li>
 <li>오픈스택스. 대학 물리학 Vol.2. 페이지 110 [웹 버전]. 원본 주소 <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>

열역학 상태 간 경로

그림 1의 AC 및 ABC 경로로 표시되는 이상 기체와 관련된 두 가지 열역학적 과정을 생각해 보세요.

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;" />

A에서 C로의 경로에 대한 첫 번째 과정에서 가스는 일정한 온도 T로 유지됩니다. V1 볼륨에서 V2 볼륨으로 확장됩니다.

이상기체가 한 일은 다음과 같이 표현된다

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;" />

이상 기체 방정식의 압력을 nRT/V로 대체하고 두 항을 적분하면 일정한 온도에서 이상 기체가 한 일은 다음과 같이 구해집니다.

<img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;" />

두 번째 과정에서는 A에서 B로 가는 경로에 대해 이상 기체가 먼저 볼륨 V1에서 열을 가해 일정한 압력 p1 에서 V2로 변환합니다. 그런 다음 가스는 B에서 C로의 경로를 따라 일정한 부피 V2로 냉각되어 압력이 p2.

A에서 B까지의 경로의 경우 작업은 지속적인 압력 하에서 수행되므로

<img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;" />

B에서 C까지의 경로에서는 부피가 일정하게 유지되므로 가스나 주변 환경에 의한 가스에 대한 작업이 수행되지 않습니다. 따라서 이 과정에서 가스가 수행한 총 일은 A 에서 B까지의 경로에서 수행한 작업과 동일합니다.

두 공정 모두에서 가스는 V1 부피에서 V2 부피로 팽창합니다. 압력이 p1에서 p2로 변경됩니다. 그러나 두 과정에서 수행되는 작업은 서로 다릅니다. 이는 시스템이 수행하는 작업이 경로에 따라 다르다는 것을 증명합니다.

그림 1에서 경로 AC 및 ABC로 표시되는 이상 기체와 관련된 두 가지 열역학 프로세스를 고려하십시오.

경로 A에서 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

The First Law of Thermodynamics

열역학 제1법칙

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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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path between thermodynamics states

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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Net Work in a Cyclic Thermodynamic Process

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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

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key terms and concepts

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Path Dependence in Gas Work | JoVE K12

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Path Dependence in Gas Work

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